{"id":1775,"date":"2020-07-31T20:35:47","date_gmt":"2020-08-01T00:35:47","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/use-the-slope-intercept-form-of-an-equation-of-a-line\/"},"modified":"2025-09-16T14:25:44","modified_gmt":"2025-09-16T18:25:44","slug":"use-the-slope-intercept-form-of-an-equation-of-a-line","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/use-the-slope-intercept-form-of-an-equation-of-a-line\/","title":{"raw":"6.5 Use the Slope\u2013Intercept Form of an Equation of a Line","rendered":"6.5 Use the Slope\u2013Intercept Form of an Equation of a Line"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section, you will be able to:\n<ul>\n \t<li>Recognize the relation between the graph and the slope\u2013intercept form of an equation of a line<\/li>\n \t<li>Identify the slope and y-intercept form of an equation of a line<\/li>\n \t<li>Graph a line using its slope and intercept<\/li>\n \t<li>Choose the most convenient method to graph a line<\/li>\n \t<li>Graph and interpret applications of slope\u2013intercept<\/li>\n \t<li>Use slopes to identify parallel lines<\/li>\n \t<li>Use slopes to identify perpendicular lines<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Recognize the Relation Between the Graph and the Slope\u2013Intercept Form of an Equation of a Line<\/h1>\n<p id=\"fs-id1169596251841\">We have graphed linear equations by plotting points, using intercepts, recognizing horizontal and vertical lines, and using the point\u2013slope method. Once we see how an equation in slope\u2013intercept form and its graph are related, we\u2019ll have one more method we can use to graph lines.<\/p>\n<p id=\"fs-id1169594172366\">In <a href=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebra1editing\/chapter\/graph-linear-equations-in-two-variables\/\">Graph Linear Equations in Two Variables<\/a>, we graphed the line of the equation \\(y=\\dfrac{1}{2}x+3\\) by plotting points. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_05_001\">(Figure)<\/a>. Let\u2019s find the slope of this line.<\/p>\n\n<div id=\"CNX_ElemAlg_Figure_04_05_001\" class=\"bc-figure figure\"><span id=\"fs-id1169594050718\" data-type=\"media\" data-alt=\"This figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The line is labeled with the equation y equals one half x, plus 3. The points (0, 3), (2, 4) and (4, 5) are labeled also. A red vertical line begins at the point (2, 4) and ends one unit above the point. It is labeled \u201cRise equals 1\u201d. A red horizontal line begins at the end of the vertical line and ends at the point (4, 5). It is labeled \u201cRun equals 2. The red lines create a right triangle with the line y equals one half x, plus 3 as the hypotenuse.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/07\/CNX_ElemAlg_Figure_04_05_001_img_new.jpg\" alt=\"This figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The line is labeled with the equation y equals one half x, plus 3. The points (0, 3), (2, 4) and (4, 5) are labeled also. A red vertical line begins at the point (2, 4) and ends one unit above the point. It is labeled \u201cRise equals 1\u201d. A red horizontal line begins at the end of the vertical line and ends at the point (4, 5). It is labeled \u201cRun equals 2. The red lines create a right triangle with the line y equals one half x, plus 3 as the hypotenuse.\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<p id=\"fs-id1169596237835\">The red lines show us the rise is 1 and the run is 2. Substituting into the slope formula:<\/p>\n\\(\\begin{array}{ccc}\\hfill m&amp; =\\hfill &amp; \\dfrac{\\text{rise}}{\\text{run}}\\hfill \\\\ \\hfill m&amp; =\\hfill &amp; \\dfrac{1}{2}\\hfill \\end{array}\\)\n<p id=\"fs-id1169594206666\">What is the <em data-effect=\"italics\">y<\/em>-intercept of the line? The <em data-effect=\"italics\">y<\/em>-intercept is where the line crosses the <em data-effect=\"italics\">y<\/em>-axis, so <em data-effect=\"italics\">y<\/em>-intercept is \\(\\left(0,3\\right)\\). The equation of this line is:<\/p>\n<span id=\"fs-id1169596364667\" data-type=\"media\" data-alt=\"The figure shows the equation y equals one half x, plus 3. The fraction one half is colored red and the number 3 is colored blue.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_034_img_new.jpg\" alt=\"The figure shows the equation y equals one half x, plus 3. The fraction one half is colored red and the number 3 is colored blue.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169594159235\">Notice, the line has:<\/p>\n<span id=\"fs-id1169596696275\" data-type=\"media\" data-alt=\"The figure shows the statement \u201cslope m equals one half and y-intercept (0, 3). The slope, one half, is colored red and the number 3 in the y-intercept is colored blue.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_035_img_new.jpg\" alt=\"The figure shows the statement \u201cslope m equals one half and y-intercept (0, 3). The slope, one half, is colored red and the number 3 in the y-intercept is colored blue.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596404951\">When a linear equation is solved for \\(y\\), the coefficient of the \\(x\\) term is the slope and the constant term is the <em data-effect=\"italics\">y<\/em>-coordinate of the <em data-effect=\"italics\">y<\/em>-intercept. We say that the equation \\(y=\\dfrac{1}{2}x+3\\) is in slope\u2013intercept form.<\/p>\n<span id=\"fs-id1169596219400\" data-type=\"media\" data-alt=\"The figure shows the statement \u201cm equals one half; y-intercept is (0, 3). The slope, one half, is colored red and the number 3 in the y-intercept is colored blue. Below that statement is the equation y equals one half x, plus 3. The fraction one half is colored red and the number 3 is colored blue. Below the equation is another equation y equals m x, plus b. The variable m is colored red and the variable b is colored blue.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_015_img_new.jpg\" alt=\"The figure shows the statement \u201cm equals one half; y-intercept is (0, 3). The slope, one half, is colored red and the number 3 in the y-intercept is colored blue. Below that statement is the equation y equals one half x, plus 3. The fraction one half is colored red and the number 3 is colored blue. Below the equation is another equation y equals m x, plus b. The variable m is colored red and the variable b is colored blue.\" data-media-type=\"image\/jpeg\"><\/span>\n<div id=\"fs-id1169596318095\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Slope-intercept form of an equation of a line<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596311488\">The slope\u2013intercept form of an equation of a line with slope \\(m\\) and <em data-effect=\"italics\">y<\/em>-intercept, \\(\\left(0,b\\right)\\) is,<\/p>\n\\(y=mx+b\\)\n\n<\/div>\n<\/div>\nSometimes the slope\u2013intercept form is called the \u201c<em>y<\/em>-form.\u201d\n\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594028925\" data-type=\"problem\">\n<p id=\"fs-id1169596698756\">Use the graph to find the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line, \\(y=2x+1\\).<\/p>\n<p id=\"fs-id1169596285072\">Compare these values to the equation\\(y=mx+b\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594011994\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596654281\">To find the slope of the line, we need to choose two points on the line. We\u2019ll use the points \\(\\left(0,1\\right)\\) and \\(\\left(1,3\\right)\\).<\/p>\n\n<table id=\"eip-id1172185589908\" class=\"unnumbered unstyled can-break\" summary=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The line is labeled with the equation y equals 2 x, plus 1. The points (negative 2, negative 3), (0, 1) and (1, 3) are plotted. Below the graph are the steps to find the slope of the line. Step 1 is the find the rise and run. The equation for slope is m equals rise divided by run. The rise is 2 and the run is 1. The slope equation becomes 2 divided by 1 which is 2. Step 2 is the find the y-intercept of the line. The y-intercept is the point (0, 1). In step 3 we compare the values found to the equation. Show in this step is the statement \u201cWe found slope m equals 2 and y-intercept is (0, 1)\u201d. The slope, 2, is colored red and the number 1 in the y-intercept is colored blue. The equation y equals 2 x, plus 3. In the equation the number 2 is colored red and the number 1 is colored blue. Below the equation is another equation y equals m x, plus b. The variable m is colored red and the variable b is colored blue.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><span id=\"eip-id1172186758147\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_016b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find the rise and run.<\/td>\n<td><span id=\"eip-id1172180058520\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_016c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187650033\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_016d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187401821\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_016e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find the <em data-effect=\"italics\">y<\/em>-intercept of the line.<\/td>\n<td data-align=\"center\">The <em data-effect=\"italics\">y<\/em>-intercept is the point (0, 1).<\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1172189015101\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_016a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><span id=\"eip-id1172185602140\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_016f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596656286\">The slope is the same as the coefficient of \\(x\\) and the <em data-effect=\"italics\">y<\/em>-coordinate of the <em data-effect=\"italics\">y<\/em>-intercept is the same as the constant term.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596292085\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594001998\" data-type=\"exercise\">\n<div id=\"fs-id1169596459717\" data-type=\"problem\">\n<p id=\"fs-id1169596382613\">Use the graph to find the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line \\(y=\\dfrac{2}{3}x-1\\). Compare these values to the equation \\(y=mx+b\\).<\/p>\n<span id=\"fs-id1169596232523\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The line goes through the points (0, negative 1) and (6, 3).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_018_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The line goes through the points (0, negative 1) and (6, 3).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id1169596687837\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596240719\">slope \\(m=\\dfrac{2}{3}\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-1\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596235127\" data-type=\"problem\">\n<p id=\"fs-id1169596395779\">Use the graph to find the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line \\(y=\\dfrac{1}{2}x+3\\). Compare these values to the equation \\(y=mx+b\\).<\/p>\n<span id=\"fs-id1169596292349\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The line goes through the points (0, 3) and (negative 6, 0).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_019_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The line goes through the points (0, 3) and (negative 6, 0).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id1169596365028\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596589952\">slope \\(m=\\dfrac{1}{2}\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,3\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Identify the Slope and <em data-effect=\"italics\">y<\/em>-Intercept From an Equation of a Line<\/h1>\n<p id=\"fs-id1169596620860\">In <a class=\"target-chapter\" href=\"\/contents\/ba42b46c-de39-4f91-a515-06bfd7a16c6b\">Understand Slope of a Line<\/a>, we graphed a line using the slope and a point. When we are given an equation in slope\u2013intercept form, we can use the <em data-effect=\"italics\">y<\/em>-intercept as the point, and then count out the slope from there. Let\u2019s practice finding the values of the slope and <em data-effect=\"italics\">y<\/em>-intercept from the equation of a line.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596551201\" data-type=\"problem\">\n<p id=\"fs-id1169596590337\">Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line with equation \\(y=-3x+5\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596530050\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596655608\">We compare our equation to the slope\u2013intercept form of the equation.<\/p>\n\n<table id=\"eip-id1172183346253\" class=\"unnumbered unstyled can-break\" style=\"width: 425px;\" summary=\"This figure has two columns. At the top of the figure, the left column says \u201cStep 1. Write the slope-intercept form of the equation of the line.\u201d The right column contains y equals mx plus b, with the variable m written in red and the variable b written in blue. One row down, the left column says \u201cStep 2. Write the equation of the line. The right column contains y equals negative 3x plus 5. Negative 3 is written in red and 5 is written in blue. One row down, the left column says \u201cStep 3. Identify the slope.\u201d The right column contains m equals negative 3. One row down, the left column says \u201cStep 4. Identify the y-intercept.\u201d The right column contains says \u201cy-intercept is (0, 5).\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 184.406px;\"><\/td>\n<td style=\"width: 211.406px;\"><span id=\"eip-id1172188022250\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_020a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 184.406px;\">Write the equation of the line.<\/td>\n<td style=\"width: 211.406px;\"><span id=\"eip-id1172187806518\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_020b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 184.406px;\">Identify the slope.<\/td>\n<td style=\"width: 211.406px;\"><span id=\"eip-id1172187837003\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_020c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 184.406px;\">Identify the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td style=\"width: 211.406px;\"><span id=\"eip-id1172184396691\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_020d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596276598\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596379858\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169594080569\">Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line \\(y=\\dfrac{2}{5}x-1\\).<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596457078\" data-type=\"solution\">\n\n\\(\\dfrac{2}{5};\\left(0,-1\\right)\\)\n\n<\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596380932\" data-type=\"problem\">\n<p id=\"fs-id1169596303982\">Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line \\(y=-\\dfrac{4}{3}x+1\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596685210\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596591237\">\\(-\\dfrac{4}{3};\\left(0,1\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\nWhen an equation of a line is not given in slope\u2013intercept form, our first step will be to solve the equation for \\(y\\).\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596299435\" data-type=\"problem\">\n<p id=\"fs-id1169596363327\">Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line with equation \\(x+2y=6\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596310364\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596387390\">This equation is not in slope\u2013intercept form. In order to compare it to the slope\u2013intercept form we must first solve the equation for\\(y\\).<\/p>\n\n<table id=\"eip-id1172187679758\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the left column says \u201cSolve for y.\u201d The right column contains the equation x plus 2y equals 6. One row down, the text in the left column says \u201cSubtract x from each side.\u201d The right column contains 2y equals negative x plus 6. One row down, the text in the left column says \u201cDivide both sides by 2.\u201d The right column contains 2y divided by 2 equals negative x plus 6 divided by 2. One row down, the text on the left says \u201cSimplify. Remember: a plus b divided by c equals a divided by c plus b divided by c.\u201d The right column contains 2y divided by 2 equals negative x divided by 2 plus 6 divided by 2. One row down, the text on the left says \u201cSimplify.\u201d The right column contains y equals negative 1 half x plus 3. One row down, the left column says \u201cWrite the slope-intercept form of the equation of the line.\u201d The right column contains y equals mx plus b, with the variable m written in red and the variable b written in blue. One row down, the text in the left column says \u201cWrite the equation of the line.\u201d The right column contains y equals negative 1 half x plus 3. Negative 1 half is written in red and 3 is written in blue. One row down, the left column says \u201cIdentify the slope.\u201d The right column contains m equals negative 1 half. One row down, the left column says \u201cIdentify the y-intercept.\u201d The right column contains says \u201cy-intercept is (0, 3).\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Solve for <em data-effect=\"italics\">y<\/em>.<\/td>\n<td>\\(x+2y=6\\)<\/td>\n<\/tr>\n<tr>\n<td>Subtract <em data-effect=\"italics\">x<\/em> from each side.<\/td>\n<td><span id=\"eip-id1172187196124\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 2.<\/td>\n<td><span id=\"eip-id1172187110656\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172187600506\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>(Remember:\\(\\dfrac{a+b}{c}=\\dfrac{a}{c}+\\dfrac{b}{c}\\))<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172186748318\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the slope\u2013intercept form of the equation of the line.<\/td>\n<td><span id=\"eip-id1172186037414\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the equation of the line.<\/td>\n<td><span id=\"eip-id1172189361890\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Identify the slope.<\/td>\n<td><span id=\"fs-id1169751895483\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Identify the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td><span id=\"fs-id1169751959438\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596622645\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594075433\" data-type=\"exercise\">\n<div id=\"fs-id1169594157418\" data-type=\"problem\">\n<p id=\"fs-id1169596765660\">Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line \\(x+4y=8\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596366913\">\\(-\\dfrac{1}{4};\\left(0,2\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594082663\" data-type=\"problem\">\n<p id=\"fs-id1169596516662\">Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line \\(3x+2y=12\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596244470\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596438180\">\\(-\\dfrac{3}{2};\\left(0,6\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Graph a Line Using its Slope and Intercept<\/h1>\n<p id=\"fs-id1169596499436\">Now that we know how to find the slope and <em data-effect=\"italics\">y<\/em>-intercept of a line from its equation, we can graph the line by plotting the <em data-effect=\"italics\">y<\/em>-intercept and then using the slope to find another point.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How to Graph a Line Using its Slope and Intercept<\/div>\n<div id=\"fs-id1169596411988\" data-type=\"exercise\">\n<div id=\"fs-id1169596593452\" data-type=\"problem\">\n<p id=\"fs-id1169596318600\">Graph the line of the equation \\(y=4x-2\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<div id=\"fs-id1169594160299\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<span id=\"fs-id1169594053951\" data-type=\"media\" data-alt=\"The figure shows the steps to graph the equation y equals 4x minus 2. Step 1 is to find the slope intercept form of the equation. The equation is already in slope intercept form.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_033a_img_new.jpg\" alt=\"The figure shows the steps to graph the equation y equals 4x minus 2. Step 1 is to find the slope intercept form of the equation. The equation is already in slope intercept form.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169594053625\" data-type=\"media\" data-alt=\"Step 2 is to identify the slope and y-intercept. Use the equation y equals m x, plus b. The equation y equals m x, plus b is shown with the variable m colored red and the variable b colored blue. Below that is the equation y equals 4 x, plus -2. The number 4 is colored red and -2 is colored blue. From this equation we can see that m equals 4 and b equals -2 so the slope is 4 and the y-intercept is the point (0, negative 2).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_033b_img_new.jpg\" alt=\"Step 2 is to identify the slope and y-intercept. Use the equation y equals m x, plus b. The equation y equals m x, plus b is shown with the variable m colored red and the variable b colored blue. Below that is the equation y equals 4 x, plus -2. The number 4 is colored red and -2 is colored blue. From this equation we can see that m equals 4 and b equals -2 so the slope is 4 and the y-intercept is the point (0, negative 2).\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596285435\" data-type=\"media\" data-alt=\"Step 3 is to plot the y-intercept. An x y-coordinate plane is shown with the x-axis of the plane running from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The point (0, negative 2) is plotted.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_033c_img_new.jpg\" alt=\"Step 3 is to plot the y-intercept. An x y-coordinate plane is shown with the x-axis of the plane running from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The point (0, negative 2) is plotted.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169594086346\" data-type=\"media\" data-alt=\"Step 4 is to use the slope formula m equals rise over run to identify the rise and the run. Since m equals 4, rise over run equals 4 over 1. From this we can determine that the rise is 4 and the run is 1.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_033d_img_new.jpg\" alt=\"Step 4 is to use the slope formula m equals rise over run to identify the rise and the run. Since m equals 4, rise over run equals 4 over 1. From this we can determine that the rise is 4 and the run is 1.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596381128\" data-type=\"media\" data-alt=\"Step 5 is to start at they-intercept, count out the rise and run to mark the second point. So start at the point (0, negative 2) and count the rise and the run. The rise is up 4 and the run is right 1. On the x y-coordinate plane is a red vertical line starts at the point (0, negative 2) and rises 4 units at its end a red horizontal line runs 1 unit to end at the point (1, 2). The point (1, 2) is plotted.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_033e_img_new.jpg\" alt=\"Step 5 is to start at they-intercept, count out the rise and run to mark the second point. So start at the point (0, negative 2) and count the rise and the run. The rise is up 4 and the run is right 1. On the x y-coordinate plane is a red vertical line starts at the point (0, negative 2) and rises 4 units at its end a red horizontal line runs 1 unit to end at the point (1, 2). The point (1, 2) is plotted.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596662513\" data-type=\"media\" data-alt=\"Step 6 is to connect the points with a line. On the x y-coordinate plane the points (0, negative 2) and (1, 2) are plotted and a line runs through the two points. The line is the graph of y equals 4 x, minus 2.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_033f_img_new.jpg\" alt=\"Step 6 is to connect the points with a line. On the x y-coordinate plane the points (0, negative 2) and (1, 2) are plotted and a line runs through the two points. The line is the graph of y equals 4 x, minus 2.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596369784\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596706450\" data-type=\"exercise\">\n<div id=\"fs-id1169596446736\" data-type=\"problem\">\n<p id=\"fs-id1169594031888\">Graph the line of the equation \\(y=4x+1\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596236687\" data-type=\"solution\"><span id=\"fs-id1169596404554\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, 1) and (1, 5) are plotted on the line.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_002_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, 1) and (1, 5) are plotted on the line.\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<div id=\"fs-id1169594149466\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594029304\" data-type=\"exercise\">\n<div id=\"fs-id1169596256256\" data-type=\"solution\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594028383\" data-type=\"problem\">\n<p id=\"fs-id1169594031441\">Graph the line of the equation \\(y=2x-3\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596256256\" data-type=\"solution\"><span id=\"fs-id1169596702940\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 3) and (1, negative 1) are plotted on the line.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_003_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 3) and (1, negative 1) are plotted on the line.\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<div id=\"fs-id1169594149466\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594029304\" data-type=\"exercise\">\n<div id=\"fs-id1169596256256\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Graph a line using its slope and <em data-effect=\"italics\">y<\/em>-intercept<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169596372582\" class=\"stepwise\" type=\"1\">\n \t<li>Find the slope-intercept form of the equation of the line.<\/li>\n \t<li>Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/li>\n \t<li>Plot the <em data-effect=\"italics\">y<\/em>-intercept.<\/li>\n \t<li>Use the slope formula \\(m=\\dfrac{\\text{rise}}{\\text{run}}\\) to identify the rise and the run.<\/li>\n \t<li>Starting at the <em data-effect=\"italics\">y<\/em>-intercept, count out the rise and run to mark the second point.<\/li>\n \t<li>Connect the points with a line.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596767304\" class=\"howto\" data-type=\"note\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596656244\" data-type=\"problem\">\n<p id=\"fs-id1169596235895\">Graph the line of the equation \\(y=-x+4\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<div id=\"fs-id1169594149555\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172184404871\" class=\"unnumbered unstyled can-break\" summary=\"This figure shows the steps to graph the equation y equals negative x plus 4. The first step is to put the equation in slope-intercept form. y equals negative x plus 4 is already in slope-intercept form. The second step is to identify the slope and y-intercept. The slope, m, equals negative 1, and the y intercept is (0, 4). The third step is to plot the y-intercept. The fourth step is to identify the rise and run, which is negative 1 over 1. Step 5 is to count out the rise and run to mark the second point, and step 6 is to draw the line. At the very bottom of the figure is a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The points (0, 4) and (1, 3) are plotted on the line.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(y=mx+b\\)<\/td>\n<\/tr>\n<tr>\n<td>The equation is in slope\u2013intercept form.<\/td>\n<td>\\(y=-x+4\\)<\/td>\n<\/tr>\n<tr>\n<td>Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td>\\(m=-1\\)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><em data-effect=\"italics\">y<\/em>-intercept is (0, 4)<\/td>\n<\/tr>\n<tr>\n<td>Plot the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td>See graph below.<\/td>\n<\/tr>\n<tr>\n<td>Identify the rise and the run.<\/td>\n<td>\\(m=\\dfrac{-1}{1}\\)<\/td>\n<\/tr>\n<tr>\n<td>Count out the rise and run to mark the second point.<\/td>\n<td>rise \u22121, run 1<\/td>\n<\/tr>\n<tr>\n<td>Draw the line.<\/td>\n<td><span id=\"eip-id1172183636610\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" data-align=\"center\">To check your work, you can find another point on the line and make sure it is a solution of the equation. In the graph we see the line goes through (4, 0).<\/td>\n<\/tr>\n<tr>\n<td>Check.\n\\(\\begin{array}{l} y =-x+4 \\\\\u00a0 0 \\stackrel{?}{=}-4+4 \\\\\u00a0 0 = 0\\checkmark \\end{array}\\)<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596446271\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596621546\" data-type=\"exercise\">\n<div id=\"fs-id1169596226960\" data-type=\"problem\">\n<p id=\"fs-id1169596702137\">Graph the line of the equation \\(y=-x-3\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596446052\" data-type=\"solution\"><span id=\"fs-id1169596554450\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 3) and (1, negative 4) are plotted on the line.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_005_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 3) and (1, negative 4) are plotted on the line.\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596764611\" data-type=\"problem\">\n<p id=\"fs-id1169596764574\">Graph the line of the equation \\(y=-x-1\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596703969\" data-type=\"solution\"><span id=\"fs-id1169596379010\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 1) and (1, negative 2) are plotted on the line.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_006_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 1) and (1, negative 2) are plotted on the line.\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594001481\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596764608\" data-type=\"exercise\">\n<div id=\"fs-id1169596703969\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594010890\" data-type=\"problem\">\n<p id=\"fs-id1169594243912\">Graph the line of the equation \\(y=-\\dfrac{2}{3}x-3\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<div id=\"fs-id1169594029231\" data-type=\"solution\">\n<div data-type=\"title\"><strong>\nSolution<\/strong><\/div>\n<table id=\"eip-id1172187131981\" class=\"unnumbered unstyled can-break\" summary=\"This figure shows the steps to graph the equation y equals negative 2 thirds x minus 3. The first step is to put the equation in slope-intercept form. y equals negative 2 thirds x minus 3 is already in slope-intercept form. The second step is to identify the slope and y-intercept. The slope, m, equals negative 2 thirds, and the y intercept is (0, negative 3). Step 4 is to count out the rise and run to mark the second point, and step 5 is to draw the line. At the very bottom of the figure is a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The points (0, negative 3) and (3, negative 5) are plotted on the line.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(y=mx+b\\)<\/td>\n<\/tr>\n<tr>\n<td>The equation is in slope\u2013intercept form.<\/td>\n<td>\\(y=-\\dfrac{2}{3}x-3\\)<\/td>\n<\/tr>\n<tr>\n<td>Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td>\\(m=-\\dfrac{2}{3}\\); <em data-effect=\"italics\">y<\/em>-intercept is (0, \u22123)<\/td>\n<\/tr>\n<tr>\n<td>Plot the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td>See graph below.<\/td>\n<\/tr>\n<tr>\n<td>Identify the rise and the run.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Count out the rise and run to mark the second point.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Draw the line.<\/td>\n<td><span id=\"eip-id1172187684428\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596655631\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596364893\" data-type=\"exercise\">\n<div id=\"fs-id1169596364896\" data-type=\"problem\">\n<p id=\"fs-id1169594002076\">Graph the line of the equation \\(y=-\\dfrac{5}{2}x+1\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596698712\" data-type=\"solution\"><span id=\"fs-id1169596235577\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0,1) and (2, negative 4) are plotted on the line.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_008_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0,1) and (2, negative 4) are plotted on the line.\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594241409\" data-type=\"problem\">\n<p id=\"fs-id1169596435270\">Graph the line of the equation \\(y=-\\dfrac{3}{4}x-2\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596648398\" data-type=\"solution\"><span id=\"fs-id1169596648402\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 2) and (4, negative 5) are plotted on the line.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_009_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 2) and (4, negative 5) are plotted on the line.\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596516694\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594241407\" data-type=\"exercise\">\n<div id=\"fs-id1169596648398\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596253295\" data-type=\"problem\">\n<p id=\"fs-id1169596253298\">Graph the line of the equation \\(4x-3y=12\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596555123\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172188103261\" class=\"unnumbered unstyled can-break\" summary=\"This figure shows the steps to graph the equation 4x minus 3y equals 12. The first step is to put the equation in slope-intercept form. Subtract 4x from both sides to get negative 3y equals negative 4x plus 12. Divide both sides by negative 3 to get y equals 4 thirds x minus 4, which is in y-intercept form. The second step is to identify the slope and y-intercept. The slope, m, equals 4 thirds, and the y intercept is (0, negative 4). Step 3 is to plot the y-intercept. Step 4 is to count out the rise and run to mark the second point, and step 5 is to draw the line. At the very bottom of the figure is a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The points (0, negative 4) and (3, 0) are plotted on the line.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(4x-3y=12\\)<\/td>\n<\/tr>\n<tr>\n<td>Find the slope\u2013intercept form of the equation.<\/td>\n<td>\\(-3y=-4x+12\\)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>\\(-\\dfrac{3y}{3}=\\dfrac{-4x+12}{-3}\\)<\/td>\n<\/tr>\n<tr>\n<td>The equation is now in slope\u2013intercept form.<\/td>\n<td>\\(y=\\dfrac{4}{3}x-4\\)<\/td>\n<\/tr>\n<tr>\n<td>Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td>\\(m=\\dfrac{4}{3}\\)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><em data-effect=\"italics\">y<\/em>-intercept is (0, \u22124)<\/td>\n<\/tr>\n<tr>\n<td>Plot the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td>See graph below.<\/td>\n<\/tr>\n<tr>\n<td>Identify the rise and the run; count out the rise and run to mark the second point.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Draw the line.<\/td>\n<td><span id=\"eip-id1172183643963\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594064448\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596348900\" data-type=\"exercise\">\n<div id=\"fs-id1169596348903\" data-type=\"problem\">\n<p id=\"fs-id1169596235492\">Graph the line of the equation \\(2x-y=6\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596377717\" data-type=\"solution\"><span id=\"fs-id1169596245210\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 6) and (1, negative 4) are plotted on the line.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_011_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 6) and (1, negative 4) are plotted on the line.\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596689546\" data-type=\"problem\">\n<p id=\"fs-id1169596689548\">Graph the line of the equation \\(3x-2y=8\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169594061626\" data-type=\"solution\"><span id=\"fs-id1169594061629\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 4) and (2, negative 1) are plotted on the line.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_012_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 4) and (2, negative 1) are plotted on the line.\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596403566\">We have used a grid with \\(x\\) and \\(y\\) both going from about \\(-10\\) to 10 for all the equations we\u2019ve graphed so far. Not all linear equations can be graphed on this small grid. Often, especially in applications with real-world data, we\u2019ll need to extend the axes to bigger positive or smaller negative numbers.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596653186\" data-type=\"problem\">\n<p id=\"fs-id1169596234434\">Graph the line of the equation \\(y=0.2x+45\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<div id=\"fs-id1169594085611\" data-type=\"solution\">\n<div data-type=\"title\"><strong>\nSolution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169594085616\">We\u2019ll use a grid with the axes going from about \\(-80\\) to 80.<\/p>\n\n<table id=\"eip-id1172183813237\" class=\"unnumbered unstyled can-break\" summary=\"This figure shows the steps to graph the equation y equals 0.2x plus 45. The first step is to put the equation in slope-intercept form. y equals 0.2x plus 45is in y-intercept form. The second step is to identify the slope and y-intercept. The slope, m, equals 0.2, and the y intercept is (0, 45). Step 3 is to plot the y-intercept. Step 4 is to count out the rise and run to mark the second point. The slope is m equals 0.2; in fraction form this means m equals 2 tenths. Given the scale of our graph, it would be easier to use the equivalent fraction m equals 10 fiftieths. Step 5 is to draw the line. At the very bottom of the figure is a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 80 to 80. The y-axis of the plane runs from negative 80 to 80. The points (0, 45) and (50, 55) are plotted on the line.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 380.406px;\"><\/td>\n<td style=\"width: 272.406px;\">\\(y=mx+b\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 380.406px;\">The equation is in slope\u2013intercept form.<\/td>\n<td style=\"width: 272.406px;\">\\(y=0.2x+45\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 380.406px;\">Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td style=\"width: 272.406px;\">\\(m=0.2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 380.406px;\"><\/td>\n<td style=\"width: 272.406px;\">The <em data-effect=\"italics\">y<\/em>-intercept is (0, 45)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 380.406px;\">Plot the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td style=\"width: 272.406px;\">See graph below.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 380.406px;\">Count out the rise and run to mark the second point. The slope is \\(m=0.2\\); in fraction form this means \\(m=\\dfrac{2}{10}\\). Given the scale of our graph, it would be easier to use the equivalent fraction \\(m=\\dfrac{10}{50}\\).<\/td>\n<td style=\"width: 272.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 380.406px;\">Draw the line.<\/td>\n<td style=\"width: 272.406px;\"><span id=\"eip-id1172184643399\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_013a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596766628\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596766631\" data-type=\"exercise\">\n<div id=\"fs-id1169594011511\" data-type=\"problem\">\n<p id=\"fs-id1169594011514\">Graph the line of the equation \\(y=0.5x+25\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596531274\" data-type=\"solution\"><span id=\"fs-id1169596531277\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 70 to 30. The y-axis of the plane runs from negative 20 to 40. The points (0, 25) and (10, 30) are plotted on the line.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_022_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 70 to 30. The y-axis of the plane runs from negative 20 to 40. The points (0, 25) and (10, 30) are plotted on the line.\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<div id=\"fs-id1169596591895\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596591898\" data-type=\"exercise\">\n<div id=\"fs-id1169594049400\" data-type=\"solution\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596591901\" data-type=\"problem\">\n<p id=\"fs-id1169596376698\">Graph the line of the equation \\(y=0.1x-30\\) using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169594049400\" data-type=\"solution\"><span id=\"fs-id1169594049403\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 50 to 350. The y-axis of the plane runs from negative 40 to 40. The points (0, negative 30) and (100, negative 20) are plotted on the line.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_023_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 50 to 350. The y-axis of the plane runs from negative 40 to 40. The points (0, negative 30) and (100, negative 20) are plotted on the line.\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<div id=\"fs-id1169596766628\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596766631\" data-type=\"exercise\">\n<div id=\"fs-id1169594011511\" data-type=\"problem\">Now that we have graphed lines by using the slope and <em data-effect=\"italics\">y<\/em>-intercept, let\u2019s summarize all the methods we have used to graph lines. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_05_038\">(Figure)<\/a>.<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596591895\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596591898\" data-type=\"exercise\">\n<div id=\"fs-id1169594049400\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Methods to graph lines<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"CNX_ElemAlg_Figure_04_05_038\" class=\"bc-figure figure\"><span id=\"fs-id1169594103513\" data-type=\"media\" data-alt=\"The table has two rows and four columns. The first row spans all four columns and is a header row. The header is \u201cMethods to Graph Lines\u201d. The second row is made up of four columns. The first column is labeled \u201cPlotting Points\u201d and shows a smaller table with four rows and two columns. The first row is a header row with the first column labeled \u201cx\u201d and the second labeled \u201cy\u201d. The rest of the table is blank. Below the table it reads \u201cFind three points. Plot the points, make sure they line up, then draw the line.\u201d The Second column is labeled \u201cSlope\u2013Intercept\u201d and shows the equation y equals m x, plus b. Below the equation it reads \u201cFind the slope and y-intercept. Start at the y-intercept, then count the slope to get a second point.\u201d The third column is labeled \u201cIntercepts\u201d and shows a smaller table with four rows and two columns. The first row is a header row with the first column labeled \u201cx\u201d and the second labeled \u201cy\u201d. The second row has a 0 in the \u201cx\u201d column and the \u201cy\u201d column is blank. The second row is blank in the \u201cx\u201d column and has a 0 in the \u201cy\u201d column. The third row is blank. Below the table it reads \u201cFind the intercepts and a third point. Plot the points, make sure they line up, then draw the line.\u201d The fourth column is labeled \u201cRecognize Vertical and Horizontal Lines\u201d. Below that it reads \u201cThe equation has only one variable.\u201d The equation x equals a is a vertical line and the equation y equals b is a horizontal line.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_038_img_new.jpg\" alt=\"The table has two rows and four columns. The first row spans all four columns and is a header row. The header is \u201cMethods to Graph Lines\u201d. The second row is made up of four columns. The first column is labeled \u201cPlotting Points\u201d and shows a smaller table with four rows and two columns. The first row is a header row with the first column labeled \u201cx\u201d and the second labeled \u201cy\u201d. The rest of the table is blank. Below the table it reads \u201cFind three points. Plot the points, make sure they line up, then draw the line.\u201d The Second column is labeled \u201cSlope\u2013Intercept\u201d and shows the equation y equals m x, plus b. Below the equation it reads \u201cFind the slope and y-intercept. Start at the y-intercept, then count the slope to get a second point.\u201d The third column is labeled \u201cIntercepts\u201d and shows a smaller table with four rows and two columns. The first row is a header row with the first column labeled \u201cx\u201d and the second labeled \u201cy\u201d. The second row has a 0 in the \u201cx\u201d column and the \u201cy\u201d column is blank. The second row is blank in the \u201cx\u201d column and has a 0 in the \u201cy\u201d column. The third row is blank. Below the table it reads \u201cFind the intercepts and a third point. Plot the points, make sure they line up, then draw the line.\u201d The fourth column is labeled \u201cRecognize Vertical and Horizontal Lines\u201d. Below that it reads \u201cThe equation has only one variable.\u201d The equation x equals a is a vertical line and the equation y equals b is a horizontal line.\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Choose the Most Convenient Method to Graph a Line<\/h1>\n<p id=\"fs-id1169596704824\">Now that we have seen several methods we can use to graph lines, how do we know which method to use for a given equation?<\/p>\n<p id=\"fs-id1169596704828\">While we could plot points, use the slope\u2013intercept form, or find the intercepts for <em data-effect=\"italics\">any<\/em> equation, if we recognize the most convenient way to graph a certain type of equation, our work will be easier. Generally, plotting points is not the most efficient way to graph a line. We saw better methods in sections 4.3, 4.4, and earlier in this section. Let\u2019s look for some patterns to help determine the most convenient method to graph a line.<\/p>\n<p id=\"fs-id1169596377609\">Here are six equations we graphed in this chapter, and the method we used to graph each of them.<\/p>\n\\(\\begin{array}{lll}&amp;\u00a0 \\textbf{Equation}\\hfill &amp; \\textbf{Method}\\hfill \\\\ \\#1\\hfill &amp; x=2\\hfill\u00a0 &amp; \\text{Vertical line}\\hfill \\\\ \\# 2\\hfill &amp; y=4\\hfill &amp; \\text{Horizontal line}\\hfill \\\\ \\#3 \\hfill &amp; -x+2y=6\\hfill &amp;\u00a0 \\text{Intercepts}\\hfill \\\\ \\#4 \\hfill &amp;\u00a0 4x-3y=12\\hfill &amp; \\text{Intercepts}\\hfill \\\\ \\#5 \\hfill &amp;y=4x-2\\hfill &amp;\u00a0 \\text{Slope\u2013intercept}\\hfill \\\\ \\#6 \\hfill &amp; y=-x+4\\hfill &amp; \\text{Slope\u2013intercept}\\hfill \\end{array}\\)\n<p id=\"fs-id1169596399223\">Equations #1 and #2 each have just one variable. Remember, in equations of this form the value of that one variable is constant; it does not depend on the value of the other variable. Equations of this form have graphs that are vertical or horizontal lines.<\/p>\n<p id=\"fs-id1169596319520\">In equations #3 and #4, both \\(x\\) and \\(y\\) are on the same side of the equation. These two equations are of the form \\(Ax+By=C\\). We substituted \\(y=0\\) to find the <em data-effect=\"italics\">x<\/em>-intercept and \\(x=0\\) to find the <em data-effect=\"italics\">y<\/em>-intercept, and then found a third point by choosing another value for \\(x\\) or \\(y\\).<\/p>\n<p id=\"fs-id1169594089163\">Equations #5 and #6 are written in slope\u2013intercept form. After identifying the slope and <em data-effect=\"italics\">y<\/em>-intercept from the equation we used them to graph the line.<\/p>\n<p id=\"fs-id1169596453279\">This leads to the following strategy.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Strategy for choosing the most convenient method to graph a line<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169594123488\">Consider the form of the equation.<\/p>\n\n<ul id=\"fs-id1169594053747\" data-bullet-style=\"bullet\">\n \t<li>If it only has one variable, it is a vertical or horizontal line.\n<ul id=\"fs-id1169596658475\" data-bullet-style=\"open-circle\">\n \t<li>\\(x=a\\) is a vertical line passing through the <em data-effect=\"italics\">x<\/em>-axis at \\(a\\).<\/li>\n \t<li>\\(y=b\\) is a horizontal line passing through the <em data-effect=\"italics\">y<\/em>-axis at \\(b\\).<\/li>\n<\/ul>\n<\/li>\n \t<li>If \\(y\\) is isolated on one side of the equation, in the form \\(y=mx+b\\), graph by using the slope and y-intercept.\n<ul id=\"fs-id1169596760713\" data-bullet-style=\"open-circle\">\n \t<li>Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept and then graph.<\/li>\n<\/ul>\n<\/li>\n \t<li>If the equation is of the form \\(Ax+By=C\\), find the intercepts.\n<ul id=\"fs-id1169596500601\" data-bullet-style=\"open-circle\">\n \t<li>Find the <em data-effect=\"italics\">x<\/em>- and <em data-effect=\"italics\">y<\/em>-intercepts, a third point, and then graph.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596591690\" data-type=\"problem\">\n<p id=\"fs-id1169596591692\">Determine the most convenient method to graph each line.<\/p>\n<p id=\"fs-id1169596395321\">a) \\(y=-6\\)\u2003b )\\(5x-3y=15\\)\u2003c) \\(x=7\\)\u2003d) \\(y=\\dfrac{2}{5}x-1\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594051521\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<ol id=\"fs-id1169597615016\" class=\"circled\" type=\"a\">\n \t<li>\\(y=-6\\)\nThis equation has only one variable,\\(y\\). Its graph is a horizontal line crossing the <em data-effect=\"italics\">y<\/em>-axis at \\(-6\\).<\/li>\n \t<li>\\(5x-3y=15\\)\nThis equation is of the form \\(Ax+By=C\\). The easiest way to graph it will be to find the intercepts and one more point.<\/li>\n \t<li>\\(x=7\\)\nThere is only one variable, \\(x\\). The graph is a vertical line crossing the <em data-effect=\"italics\">x<\/em>-axis at 7.<\/li>\n \t<li>\\(y=\\dfrac{2}{5}x-1\\)\nSince this equation is in \\(y=mx+b\\) form, it will be easiest to graph this line by using the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596361008\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596438942\" data-type=\"exercise\">\n<div id=\"fs-id1169596438944\" data-type=\"problem\">\n<p id=\"fs-id1169596438946\">Determine the most convenient method to graph each line: a) \\(3x+2y=12\\)\u2003b) \\(y=4\\)\u2003c) \\(y=\\dfrac{1}{5}x-4\\)\u2003d) \\(x=-7\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594053830\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594053833\">a) intercepts\u2003b) horizontal line\u2003c) slope\u2013intercept\u2003d) vertical line<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594051697\" data-type=\"problem\">\n<p id=\"fs-id1169594160383\">Determine the most convenient method to graph each line: a) \\(x=6\\)\u2003b) \\(y=-\\dfrac{3}{4}x+1\\)\u2003c) \\(y=-8\\)\u2003d) \\(4x-3y=-1\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594112314\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594085183\">a) vertical line\u2003b) slope\u2013intercept\u2003c) horizontal line\u2003d) intercepts<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Graph and Interpret Applications of Slope\u2013Intercept<\/h1>\n<p id=\"fs-id1169596453823\">Many real-world applications are modeled by linear equations. We will take a look at a few applications here so you can see how equations written in slope\u2013intercept form relate to real-world situations.<\/p>\n<p id=\"fs-id1169594028785\">Usually when a linear equation models a real-world situation, different letters are used for the variables, instead of <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em>. The variable names remind us of what quantities are being measured.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596569131\" data-type=\"problem\">\n<p id=\"fs-id1169596569133\">The equation \\(F=\\dfrac{9}{5}C+32\\) is used to convert temperatures, \\(C\\), on the Celsius scale to temperatures, \\(F\\), on the Fahrenheit scale.<\/p>\n<p id=\"fs-id1169751874566\">a) Find the Fahrenheit temperature for a Celsius temperature of 0.\nb) Find the Fahrenheit temperature for a Celsius temperature of 20.\nc) Interpret the slope and <em data-effect=\"italics\">F<\/em>-intercept of the equation.\nd) Graph the equation.<\/p>\n&nbsp;\n\n<\/div>\n<div id=\"fs-id1169596381060\" data-type=\"solution\">\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-765\" summary=\".\">\n<tbody>\n<tr>\n<td>a)\nFind the Fahrenheit temperature for a Celsius temperature of 0.\nFind \\(F\\) when \\(C=0\\).\nSimplify.<\/td>\n<td>\\(\\begin{array}{c}F=\\dfrac{9}{5}C+32\\hfill \\\\ F=\\dfrac{9}{5}\\left(0\\right)+32\\hfill \\\\ F=32\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>b)\nFind the Fahrenheit temperature for a Celsius temperature of 20.\nFind \\(F\\) when \\(C=20\\).\nSimplify.\nSimplify.<\/td>\n<td>\\(\\begin{array}{c}F=\\dfrac{9}{5}C+32\\hfill \\\\ F=\\dfrac{9}{5}\\left(20\\right)+32\\hfill \\\\ F=36+32\\hfill \\\\ F=68\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596389972\">c) Interpret the slope and <em data-effect=\"italics\">F<\/em>-intercept of the equation.<\/p>\n<p id=\"fs-id1169596653603\">Even though this equation uses \\(F\\)and \\(C\\), it is still in slope\u2013intercept form.<\/p>\n<span id=\"fs-id1169596515134\" data-type=\"media\" data-alt=\"This image shows three lines of equations. The first line reads y equals m x plus b. The second line reads F equals m C plus b and the third line reads F equals nine fifths times C plus 32.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_024_img_new.jpg\" alt=\"This image shows three lines of equations. The first line reads y equals m x plus b. The second line reads F equals m C plus b and the third line reads F equals nine fifths times C plus 32.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596372283\">The slope, \\(\\dfrac{9}{5}\\), means that the temperature Fahrenheit (<em data-effect=\"italics\">F<\/em>) increases 9 degrees when the temperature Celsius (<em data-effect=\"italics\">C<\/em>) increases 5 degrees.<\/p>\n<p id=\"fs-id1169594008570\">The <em data-effect=\"italics\">F<\/em>-intercept means that when the temperature is 0\u00b0 on the Celsius scale, it is 32\u00b0 on the Fahrenheit scale.<\/p>\n<p id=\"fs-id1169596623952\">d) Graph the equation.<\/p>\n<p id=\"fs-id1169594002104\">We\u2019ll need to use a larger scale than our usual. Start at the <em data-effect=\"italics\">F<\/em>-intercept \\(\\left(0,32\\right)\\) then count out the rise of 9 and the run of 5 to get a second point. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_05_039\">(Figure)<\/a>.<\/p>\n\n<div id=\"CNX_ElemAlg_Figure_04_05_039\" class=\"bc-figure figure\"><span id=\"fs-id1169596400346\" data-type=\"media\" data-alt=\"No Alt Text\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_039_img_new.jpg\" alt=\"No Alt Text\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596531828\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596687493\" data-type=\"exercise\">\n<div id=\"fs-id1169596687495\" data-type=\"problem\">\n<p id=\"fs-id1169596687497\">The equation \\(h=2s+50\\) is used to estimate a woman\u2019s height in inches, <em data-effect=\"italics\">h<\/em>, based on her shoe size, <em data-effect=\"italics\">s<\/em>.<\/p>\n<p id=\"fs-id1169751902824\">a) Estimate the height of a child who wears women\u2019s shoe size 0.\nb) Estimate the height of a woman with shoe size 8.\nc) Interpret the slope and <em data-effect=\"italics\">h<\/em>-intercept of the equation.\nd) Graph the equation.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596534829\" data-type=\"solution\">\n<ol id=\"fs-id1169597594096\" class=\"circled\" type=\"a\">\n \t<li>50 inches<\/li>\n \t<li>66 inches<\/li>\n \t<li>The slope, 2, means that the height, <em data-effect=\"italics\">h<\/em>, increases by 2 inches when the shoe size, <em data-effect=\"italics\">s<\/em>, increases by 1. The <em data-effect=\"italics\">h<\/em>-intercept means that when the shoe size is 0, the height is 50 inches.<\/li>\n \t<li><span id=\"fs-id1169594029134\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable s and runs from negative 2 to 15. The y-axis of the plane represents the variable h and runs from negative 1 to 80. The line begins at the point (0, 50) and goes through the points (8, 66).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_026_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable s and runs from negative 2 to 15. The y-axis of the plane represents the variable h and runs from negative 1 to 80. The line begins at the point (0, 50) and goes through the points (8, 66).\" data-media-type=\"image\/jpeg\"><\/span><\/li>\n<\/ol>\n<\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596593374\" data-type=\"problem\">\n<p id=\"fs-id1169596593376\">The equation \\(T=\\dfrac{1}{4}n+40\\) is used to estimate the temperature in degrees Fahrenheit, <em data-effect=\"italics\">T<\/em>, based on the number of cricket chirps, <em data-effect=\"italics\">n<\/em>, in one minute.<\/p>\n<p id=\"fs-id1169751956325\">a) Estimate the temperature when there are no chirps.\nb) Estimate the temperature when the number of chirps in one minute is 100.\nc) Interpret the slope and <em data-effect=\"italics\">T<\/em>-intercept of the equation.\nd) Graph the equation.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169594137644\" data-type=\"solution\">\n<ol id=\"fs-id1169597818415\" class=\"circled\" type=\"a\">\n \t<li>40 degrees<\/li>\n \t<li>65 degrees<\/li>\n \t<li>The slope, \\(\\dfrac{1}{4}\\), means that the temperature Fahrenheit (<em data-effect=\"italics\">F<\/em>) increases 1 degree when the number of chirps, <em data-effect=\"italics\">n<\/em>, increases by 4. The <em data-effect=\"italics\">T<\/em>-intercept means that when the number of chirps is 0, the temperature is 40\u00b0.<\/li>\n \t<li><span id=\"fs-id1169596648790\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable n and runs from 10 to 140 The y-axis of the plane represents the variable T and runs from negative 5 to 75. The line begins at the point (0, 40) and goes through the point (100, 65).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_027_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable n and runs from 10 to 140 The y-axis of the plane represents the variable T and runs from negative 5 to 75. The line begins at the point (0, 40) and goes through the point (100, 65).\" data-media-type=\"image\/jpeg\"><\/span><\/li>\n<\/ol>\n<\/div>\n<\/details><\/div>\n<\/div>\n<p id=\"fs-id1169596468179\">The cost of running some types business has two components\u2014a <em data-effect=\"italics\">fixed cost<\/em> and a <em data-effect=\"italics\">variable cost<\/em>. The fixed cost is always the same regardless of how many units are produced. This is the cost of rent, insurance, equipment, advertising, and other items that must be paid regularly. The variable cost depends on the number of units produced. It is for the material and labour needed to produce each item.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596395176\" data-type=\"problem\">\n<p id=\"fs-id1169596395178\">Stella has a home business selling gourmet pizzas. The equation \\(C=4p+25\\) models the relation between her weekly cost, <em data-effect=\"italics\">C<\/em>, in dollars and the number of pizzas, <em data-effect=\"italics\">p<\/em>, that she sells.<\/p>\n<p id=\"fs-id1169754417036\">a) Find Stella\u2019s cost for a week when she sells no pizzas.\nb) Find the cost for a week when she sells 15 pizzas.\nc) Interpret the slope and <em data-effect=\"italics\">C<\/em>-intercept of the equation.\nd) Graph the equation.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596765745\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172182381935\" class=\"unnumbered unstyled can-break\" summary=\"This figure shows the steps to solve a four part problem. Part (a) is to find Stella\u2019s cost for a week when she sells no pizzas. The equation is C equals 4p plus 25, where C is Stella\u2019s cost and p is the number of pizzas sold. We must find C when p equals 0. Solving for C in the equation C equals 4 times 0 plus 25 yields a value of 25 for C. Stella\u2019s weekly cost is ?25 when she sells no pizzas. Part (b) is to find Stella\u2019s cost for a week when she sells 15 pizzas. Solving for C in the equation C equals 4 times 15 plus 25 yields C equals 60 plus 25 plus 32, which we simplify to C equals 85. Stella\u2019s weekly cost is ?85 when she sells no pizzas. Part (c) is to interpret the slope and C-intercept of the equation. Even though the equation C equals 4p plus 25 uses C and p, it is still in slope-intercept form. The slope, 4, means that the cost increases by ?4 for each pizza Stella sells. The C-intercept means that even when Stella sells no pizzas, her costs for the week are ?25. Part (d) is to graph the equation. We\u2019ll need to use a larger scale than our usual. Start at the C-intercept (0, 25) then count out the rise of 5 and the run of 1 to get a second point. At the very bottom of the figure is a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable p and runs from negative 1 to 20. The y-axis of the plane represents the variable C and runs from negative 1 to 100. The line begins at the point (0, 25) and goes through the point (15, 85).\" data-label=\"\">\n<tbody>\n<tr>\n<td>a) Find Stella's cost for a week when she sells no pizzas.<\/td>\n<td><span id=\"eip-id1172185620920\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find <em data-effect=\"italics\">C<\/em> when \\(p=0\\).<\/td>\n<td><span id=\"eip-id1172185620945\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172185620962\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Stella's fixed cost is \\$25 when she sells no pizzas.<\/td>\n<\/tr>\n<tr>\n<td>b) Find the cost for a week when she sells 15 pizzas.<\/td>\n<td><span id=\"eip-id1172182578628\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find <em data-effect=\"italics\">C<\/em> when \\(p=15\\).<\/td>\n<td><span id=\"eip-id1172182578653\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172180200408\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172180200424\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Stella's costs are \\$85 when she sells 15 pizzas.<\/td>\n<\/tr>\n<tr>\n<td>c) Interpret the slope and <em data-effect=\"italics\">C<\/em>-intercept of the equation.<\/td>\n<td><span id=\"eip-id1172189350891\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>The slope, 4, means that the cost increases by \\$4 for each pizza Stella sells. The <em data-effect=\"italics\">C<\/em>-intercept means that even when Stella sells no pizzas, her costs for the week are \\$25.<\/td>\n<\/tr>\n<tr>\n<td>d) Graph the equation. We'll need to use a larger scale than our usual. Start at the <em data-effect=\"italics\">C<\/em>-intercept (0, 25) then count out the rise of 4 and the run of 1 to get a second point.<\/td>\n<td><span id=\"eip-id1172189350923\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596653516\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596653520\" data-type=\"exercise\">\n<div id=\"fs-id1169596653523\" data-type=\"problem\">\n<p id=\"fs-id1169596375236\">Sam drives a delivery van. The equation \\(C=0.5m+60\\) models the relation between his weekly cost, <em data-effect=\"italics\">C<\/em>, in dollars and the number of miles, <em data-effect=\"italics\">m<\/em>, that he drives.<\/p>\n<p id=\"fs-id1169751894665\">a) Find Sam\u2019s cost for a week when he drives 0 miles.\nb) Find the cost for a week when he drives 250 miles.\nc) Interpret the slope and <em data-effect=\"italics\">C<\/em>-intercept of the equation.\nd) Graph the equation.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id11695941759711\" data-type=\"solution\">\n<ol id=\"fs-id1169597517137\" class=\"circled\" type=\"a\">\n \t<li>\\$60<\/li>\n \t<li>\\$185<\/li>\n \t<li>The slope, 0.5, means that the weekly cost, <em data-effect=\"italics\">C<\/em>, increases by \\$0.50 when the number of miles driven, <em data-effect=\"italics\">n,<\/em> increases by 1. The <em data-effect=\"italics\">C<\/em>-intercept means that when the number of miles driven is 0, the weekly cost is \\$60<\/li>\n \t<li><span id=\"fs-id1169594007893\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 10 to 400. The y-axis of the plane represents the variable C and runs from negative 10 to 300. The line begins at the point (0, 65) and goes through the point (250, 185).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_036_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 10 to 400. The y-axis of the plane represents the variable C and runs from negative 10 to 300. The line begins at the point (0, 65) and goes through the point (250, 185).\" data-media-type=\"image\/jpeg\"><\/span><\/li>\n<\/ol>\n<\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596555224\" data-type=\"problem\">\n<p id=\"fs-id1169596555226\">Loreen has a calligraphy business. The equation \\(C=1.8n+35\\) models the relation between her weekly cost, <em data-effect=\"italics\">C<\/em>, in dollars and the number of wedding invitations, <em data-effect=\"italics\">n<\/em>, that she writes.<\/p>\n<p id=\"fs-id1169751961255\">a) Find Loreen\u2019s cost for a week when she writes no invitations.\nb) Find the cost for a week when she writes 75 invitations.\nc) Interpret the slope and <em data-effect=\"italics\">C<\/em>-intercept of the equation.\nd) Graph the equation.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169594050309\" data-type=\"solution\">\n<ol id=\"fs-id1169595118573\" class=\"circled\" type=\"a\">\n \t<li>\\$35<\/li>\n \t<li>\\$170<\/li>\n \t<li>The slope, 1.8, means that the weekly cost, C, increases by \\$1.80 when the number of invitations, <em data-effect=\"italics\">n<\/em>, increases by 1.80.\nThe <em data-effect=\"italics\">C<\/em>-intercept means that when the number of invitations is 0, the weekly cost is \\$35.;<\/li>\n \t<li><span id=\"fs-id1169594028669\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable n and runs from negative 10 to 400. The y-axis of the plane represents the variable C and runs from negative 10 to 300. The line begins at the point (0, 35) and goes through the point (75, 170).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_037_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable n and runs from negative 10 to 400. The y-axis of the plane represents the variable C and runs from negative 10 to 300. The line begins at the point (0, 35) and goes through the point (75, 170).\" data-media-type=\"image\/jpeg\"><\/span><\/li>\n<\/ol>\n<\/div>\n<\/details><\/div>\n<\/div>\n<h1 data-type=\"title\">Use Slopes to Identify Parallel Lines<\/h1>\n<p id=\"fs-id1169596379736\">The slope of a line indicates how steep the line is and whether it rises or falls as we read it from left to right. Two lines that have the same slope are called parallel lines. Parallel lines never intersect.<\/p>\n<span id=\"fs-id1169594029149\" data-type=\"media\" data-alt=\"The figure shows three pairs of lines side-by-side. The pair of lines on the left run diagonally rising from left to right. The pair run side-by-side, not crossing. The pair of lines in the middle run diagonally dropping from left to right. The pair run side-by-side, not crossing. The pair of lines on the right run diagonally also dropping from left to right, but with a lesser slope. The pair run side-by-side, not crossing.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_029_img_new.jpg\" alt=\"The figure shows three pairs of lines side-by-side. The pair of lines on the left run diagonally rising from left to right. The pair run side-by-side, not crossing. The pair of lines in the middle run diagonally dropping from left to right. The pair run side-by-side, not crossing. The pair of lines on the right run diagonally also dropping from left to right, but with a lesser slope. The pair run side-by-side, not crossing.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596394539\">We say this more formally in terms of the rectangular coordinate system. Two lines that have the same slope and different <em data-effect=\"italics\">y<\/em>-intercepts are called parallel lines. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_05_030\">(Figure)<\/a>.<\/p>\nVerify that both lines have the same slope, \\(m=\\dfrac{2}{5}\\), and different <em data-effect=\"italics\">y<\/em>-intercepts.\n<div id=\"CNX_ElemAlg_Figure_04_05_030\" class=\"bc-figure figure\">\n\n<span id=\"fs-id1169596658723\" data-type=\"media\" data-alt=\"The figure shows two lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line goes through the points (negative 5,1) and (5,5). The other line goes through the points (negative 5, negative 4) and (5,0).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_030_img_new.jpg\" alt=\"The figure shows two lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line goes through the points (negative 5,1) and (5,5). The other line goes through the points (negative 5, negative 4) and (5,0).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<p id=\"fs-id1169594079040\">What about vertical lines? The slope of a vertical line is undefined, so vertical lines don\u2019t fit in the definition above. We say that vertical lines that have different <em data-effect=\"italics\">x<\/em>-intercepts are parallel. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_05_031\">(Figure)<\/a>.<\/p>\nVertical lines with different <em data-effect=\"italics\">x<\/em>-intercepts are parallel.\n<div id=\"CNX_ElemAlg_Figure_04_05_031\" class=\"bc-figure figure\">\n\n<span id=\"fs-id1169596445986\" data-type=\"media\" data-alt=\"The figure shows two vertical lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line goes through the points (2,1) and (2,5). The other line goes through the points (5, negative 4) and (5,0).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_031_img_new.jpg\" alt=\"The figure shows two vertical lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line goes through the points (2,1) and (2,5). The other line goes through the points (5, negative 4) and (5,0).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id1169596767400\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Parallel lines<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596767406\">Parallel lines are lines in the same plane that do not intersect.<\/p>\n\n<ul id=\"fs-id1169596765521\" data-bullet-style=\"bullet\">\n \t<li>Parallel lines have the same slope and different <em data-effect=\"italics\">y<\/em>-intercepts.<\/li>\n \t<li>If \\({m}_{1}\\) and \\({m}_{2}\\) are the slopes of two parallel lines then\\({m}_{1}={m}_{2}\\).<\/li>\n \t<li>Parallel vertical lines have different <em data-effect=\"italics\">x<\/em>-intercepts.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169594176048\">Let\u2019s graph the equations \\(y=-2x+3\\) and \\(2x+y=-1\\) on the same grid. The first equation is already in slope\u2013intercept form: \\(y=-2x+3\\). We solve the second equation for \\(y\\):<\/p>\n\\(\\begin{array}{ccc}\\hfill 2x+y&amp; =\\hfill &amp; -1\\hfill \\\\ \\hfill y&amp; =\\hfill &amp; -2x-1\\hfill \\end{array}\\)\n<p id=\"fs-id1169596437484\">Graph the lines.<\/p>\n<span id=\"fs-id1169596437487\" data-type=\"media\" data-alt=\"The figure shows two lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line goes through the points (negative 4, 7) and (3, negative 7). The other line goes through the points (negative 2, 7) and (5, negative 7).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_032_img_new.jpg\" alt=\"The figure shows two lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line goes through the points (negative 4, 7) and (3, negative 7). The other line goes through the points (negative 2, 7) and (5, negative 7).\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169594123582\">Notice the lines look parallel. What is the slope of each line? What is the <em data-effect=\"italics\">y<\/em>-intercept of each line?<\/p>\n\\(\\begin{array}{cclccl}y&amp;=&amp; mx+b \\qquad &amp; \\qquad\u00a0 y&amp; =&amp; mx+b \\\\ y &amp; = &amp; -2x+3 \\qquad &amp; \\qquad y&amp;= &amp; -2x-1 \\\\\u00a0 m&amp; = &amp; -2 \\qquad &amp; \\qquad m&amp; = &amp; -2 \\\\ b&amp; = &amp; 3,\\text{(0, 3)}\\qquad &amp; \\qquad b &amp; = &amp; -1,\\text{(0, -1)}\\hfill \\end{array}\\)\n<p id=\"fs-id1169596296181\">The slopes of the lines are the same and the <em data-effect=\"italics\">y<\/em>-intercept of each line is different. So we know these lines are parallel.<\/p>\n<p id=\"fs-id1169594083617\">Since parallel lines have the same slope and different <em data-effect=\"italics\">y<\/em>-intercepts, we can now just look at the slope\u2013intercept form of the equations of lines and decide if the lines are parallel.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594083633\" data-type=\"problem\">\n<p id=\"fs-id1169594160247\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines \\(3x-2y=6\\) and \\(y=\\dfrac{3}{2}x+1\\) are parallel.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596244418\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-562\" summary=\"\/\">\n<tbody>\n<tr>\n<td>Solve the first equation for \\(y\\).<\/td>\n<td>\\(\\begin{array}{rcl} 3x-2y&amp; = &amp; 6 \\\\\u00a0 -2y&amp; = &amp; -3x+6 \\\\\u00a0 \\dfrac{-2y}{-2}&amp; = &amp; \\dfrac{-3x+6}{-2} \\end{array}\\)<\/td>\n<td>and<\/td>\n<td>\\(y=\\dfrac{3}{2}x+1\\)<\/td>\n<\/tr>\n<tr>\n<td>The equation is now in slope-intercept form.<\/td>\n<td>\\(y=\\dfrac{3}{2}x-3\\)<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The equation of the second line is already in slope-intercept form.<\/td>\n<td><\/td>\n<td><\/td>\n<td>\\(y=\\dfrac{3}{2}x+1\\)<\/td>\n<\/tr>\n<tr>\n<td>Identify the slope and \\(y\\)-intercept of both lines.<\/td>\n<td>\\(\\begin{array}{l} \\\\ \\\\ \\\\ y=\\dfrac{3}{2}x-3\\hfill \\\\\u00a0 y=mx+b\\hfill \\\\ m=\\dfrac{3}{2}\\hfill \\end{array}\\)<\/td>\n<td><\/td>\n<td>\\(\\begin{array}{l}y=\\dfrac{3}{2}x+1\\hfill \\\\ y=mx+b\\hfill \\\\ m=\\dfrac{3}{2}\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>y-intercept is (0, \u22123)<\/td>\n<td><\/td>\n<td>y-intercept is (0, 1)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594178196\">The lines have the same slope and different <em data-effect=\"italics\">y<\/em>-intercepts and so they are parallel. You may want to graph the lines to confirm whether they are parallel.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594178209\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594178213\" data-type=\"exercise\">\n<div id=\"fs-id1169594178215\" data-type=\"problem\">\n<p id=\"fs-id1169594178217\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines \\(2x+5y=5\\) and \\(y=-\\dfrac{2}{5}x-4\\) are parallel.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596535500\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596535502\">parallel<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596535514\" data-type=\"problem\">\n<p id=\"fs-id1169596535516\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines \\(4x-3y=6\\) and \\(y=\\dfrac{4}{3}x-1\\) are parallel.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596446494\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596446496\">parallel<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596535508\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596535512\" data-type=\"exercise\">\n<div id=\"fs-id1169596446494\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596685319\" data-type=\"problem\">\n<p id=\"fs-id1169596685321\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines \\(y=-4\\) and \\(y=3\\) are parallel.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596445675\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-410\" summary=\"\/\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\begin{array}{c}y=-4\\hfill \\\\ y=0x-4\\hfill \\end{array}\\)<\/td>\n<td>and<\/td>\n<td>\\(\\begin{array}{c}y=3\\hfill \\\\ y=0x+3\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>Write each equation in slope-intercept form.<\/td>\n<td>\\(y=0x-4\\)<\/td>\n<td><\/td>\n<td>\\(y=0x+3\\)<\/td>\n<\/tr>\n<tr>\n<td>Since there is no \\(x\\) term we write \\(0x\\).<\/td>\n<td>\\(y=mx+b\\)<\/td>\n<td><\/td>\n<td>\\(y=mx+b\\)<\/td>\n<\/tr>\n<tr>\n<td>Identify the slope and \\(y\\)-intercept of both lines.<\/td>\n<td>\\(m=0\\)<\/td>\n<td><\/td>\n<td>\\(m=0\\)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>y-intercept is (0, 4)<\/td>\n<td><\/td>\n<td>y-intercept is (0, 3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594137437\">The lines have the same slope and different <em data-effect=\"italics\">y<\/em>-intercepts and so they are parallel.<\/p>\n<p id=\"fs-id1169594137460\">There is another way you can look at this example. If you recognize right away from the equations that these are horizontal lines, you know their slopes are both 0. Since the horizontal lines cross the <em data-effect=\"italics\">y<\/em>-axis at \\(y=-4\\) and at \\(y=3\\), we know the <em data-effect=\"italics\">y<\/em>-intercepts are \\(\\left(0,-4\\right)\\) and \\(\\left(0,3\\right)\\). The lines have the same slope and different <em data-effect=\"italics\">y<\/em>-intercepts and so they are parallel.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596446494\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596446319\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596446324\" data-type=\"exercise\">\n<div id=\"fs-id1169596446326\" data-type=\"problem\">\n<p id=\"fs-id1169596365608\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines \\(y=8\\) and \\(y=-6\\) are parallel.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596365636\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596457923\">parallel<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596457936\" data-type=\"problem\">\n<p id=\"fs-id1169596457938\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines \\(y=1\\) and \\(y=-5\\) are parallel.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596371937\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596371939\">parallel<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596457930\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596457934\" data-type=\"exercise\">\n<div id=\"fs-id1169596371937\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169595152111\" data-type=\"problem\">\n<p id=\"fs-id1169596371952\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines \\(x=-2\\) and \\(x=-5\\) are parallel.<\/p>\n\n<\/div>\n<div id=\"fs-id1169594188927\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<div id=\"fs-id1169596634997\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(x=-2\\) and \\(x=-5\\)<\/div>\n<p id=\"fs-id1169596635017\">Since there is no\\(y\\), the equations cannot be put in slope\u2013intercept form. But we recognize them as equations of vertical lines. Their <em data-effect=\"italics\">x<\/em>-intercepts are \\(-2\\) and \\(-5\\). Since their <em data-effect=\"italics\">x<\/em>-intercepts are different, the vertical lines are parallel.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594060048\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594060052\" data-type=\"exercise\">\n<div id=\"fs-id1169594030452\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594060048\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594060052\" data-type=\"exercise\">\n<div id=\"fs-id1169594030452\" data-type=\"problem\">\n<p id=\"fs-id1169594030454\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines \\(x=1\\) and \\(x=-5\\) are parallel.<\/p>\n\n<\/div>\n<div id=\"fs-id1169594087033\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594087035\">parallel<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594087048\" data-type=\"problem\">\n<p id=\"fs-id1169594087050\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines \\(x=8\\) and \\(x=-6\\) are parallel.<\/p>\n\n<\/div>\n<div id=\"fs-id1169594158056\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594158058\">parallel<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594087042\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594087046\" data-type=\"exercise\">\n<div id=\"fs-id1169594158056\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594158069\" data-type=\"problem\">\n<p id=\"fs-id1169594158071\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines \\(y=2x-3\\) and \\(-6x+3y=-9\\) are parallel. You may want to graph these lines, too, to see what they look like.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596438801\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-771\" style=\"width: 789px; height: 255px;\" summary=\".\">\n<tbody>\n<tr>\n<td style=\"width: 165.406px;\"><\/td>\n<td style=\"width: 197.406px;\">\\(y=2x-3\\)<\/td>\n<td style=\"width: 34.4062px;\">and<\/td>\n<td style=\"width: 332.406px;\">\\(-6x+3y=-9\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 165.406px;\">The first equation is already in slope-intercept form.<\/td>\n<td style=\"width: 197.406px;\">\\(y=2x-3\\)<\/td>\n<td style=\"width: 34.4062px;\"><\/td>\n<td style=\"width: 332.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 165.406px;\">Solve the second equation for \\(y\\).<\/td>\n<td style=\"width: 197.406px;\"><\/td>\n<td style=\"width: 34.4062px;\"><\/td>\n<td style=\"width: 332.406px;\">\\(\\begin{array}{ccc} -6x+3y&amp; = &amp; -9 \\\\\u00a0 3y&amp; = &amp; 6x-9 \\\\\u00a0 \\dfrac{3y}{3}&amp; = &amp; \\dfrac{6x-9}{3} \\\\\u00a0 y&amp; = &amp; 2x-3 \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 165.406px;\">The second equation is now in slope-intercept form.<\/td>\n<td style=\"width: 197.406px;\">\\(y=2x-3\\)<\/td>\n<td style=\"width: 34.4062px;\"><\/td>\n<td style=\"width: 332.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 165.406px;\">Identify the slope and \\(y\\)-intercept of both lines.<\/td>\n<td style=\"width: 197.406px;\">\\(\\begin{array}{l} y =2x-3 \\\\\u00a0 y=mx+b\\\\\u00a0 m =2 \\end{array}\\)<\/td>\n<td style=\"width: 34.4062px;\"><\/td>\n<td style=\"width: 332.406px;\">\\(\\begin{array}{l} y=2x-3 \\\\\u00a0 y=mx+b \\\\\u00a0 m=2 \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 165.406px;\"><\/td>\n<td style=\"width: 197.406px;\">\\(y\\text{-intercept is (0, -3)}\\)<\/td>\n<td style=\"width: 34.4062px;\"><\/td>\n<td style=\"width: 332.406px;\">\\(y\\text{-intercept is (0, -3)}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596445891\">The lines have the same slope, but they also have the same <em data-effect=\"italics\">y<\/em>-intercepts. Their equations represent the same line. They are not parallel; they are the same line.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596445904\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596445908\" data-type=\"exercise\">\n<div id=\"fs-id1169596445910\" data-type=\"problem\">\n<p id=\"fs-id1169596445912\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines \\(y=-\\dfrac{1}{2}x-1\\) and \\(x+2y=2\\) are parallel.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596445997\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596445999\">not parallel; same line<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596446012\" data-type=\"problem\">\n<p id=\"fs-id1169596446014\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines \\(y=\\dfrac{3}{4}x-3\\) and \\(3x-4y=12\\) are parallel.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596215980\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596215982\">not parallel; same line<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Use Slopes to Identify Perpendicular Lines<\/h1>\n<p id=\"fs-id1169596754462\">Let\u2019s look at the lines whose equations are \\(y=\\dfrac{1}{4}x-1\\) and \\(y=-4x+2\\), shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_05_033\">(Figure)<\/a>.<\/p>\n\n<div id=\"CNX_ElemAlg_Figure_04_05_033\" class=\"bc-figure figure\"><span id=\"fs-id1169596648808\" data-type=\"media\" data-alt=\"The figure shows two lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line is labeled with the equation y equals negative 4x plus 2 and goes through the points (0,2) and (1, negative 2). The other line is labeled with the equation y equals one fourth x minus 1 and goes through the points (0, negative 1) and (4,0).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_033_img_new.jpg\" alt=\"The figure shows two lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line is labeled with the equation y equals negative 4x plus 2 and goes through the points (0,2) and (1, negative 2). The other line is labeled with the equation y equals one fourth x minus 1 and goes through the points (0, negative 1) and (4,0).\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<p id=\"fs-id1169596648827\">These lines lie in the same plane and intersect in right angles. We call these lines perpendicular.<\/p>\n<p id=\"fs-id1169594178156\">What do you notice about the slopes of these two lines? As we read from left to right, the line \\(y=\\dfrac{1}{4}x-1\\) rises, so its slope is positive. The line\\(y=-4x+2\\) drops from left to right, so it has a negative slope. Does it make sense to you that the slopes of two perpendicular lines will have opposite signs?<\/p>\n<p id=\"fs-id1169596754391\">If we look at the slope of the first line, \\({m}_{1}=\\dfrac{1}{4}\\), and the slope of the second line, \\({m}_{2}=-4\\), we can see that they are <em data-effect=\"italics\">negative reciprocals<\/em> of each other. If we multiply them, their product is \\(-1\\).<\/p>\n<p style=\"text-align: center;\">\\(\\begin{array}{c}{m}_{1}\\cdot {m}_{2} \\\\ \\dfrac{1}{4}\\left(-4\\right)\\hfill \\\\ -1\\hfill \\end{array}\\)<\/p>\n<p id=\"fs-id1169594243066\">This is always true for <span class=\"no-emphasis\" data-type=\"term\">perpendicular lines<\/span> and leads us to this definition.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Perpendicular lines<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169594243075\"><strong data-effect=\"bold\">Perpendicular lines<\/strong> are lines in the same plane that form a right angle.<\/p>\n<p id=\"fs-id1169594243080\">If \\({m}_{1}\\) and \\({m}_{2}\\) are the slopes of two perpendicular lines, then:<\/p>\n\\({m}_{1}\\cdot {m}_{2}=-1\\) and \\({m}_{1}=\\dfrac{-1}{{m}_{2}}\\)\n<p id=\"fs-id1169596598032\">Vertical lines and horizontal lines are always perpendicular to each other.<\/p>\n\n<\/div>\n<\/div>\n<p id=\"fs-id1169596598036\">We were able to look at the slope\u2013intercept form of linear equations and determine whether or not the lines were parallel. We can do the same thing for perpendicular lines.<\/p>\n<p id=\"fs-id1169596598043\">We find the slope\u2013intercept form of the equation, and then see if the slopes are negative reciprocals. If the product of the slopes is \\(-1\\), the lines are perpendicular. Perpendicular lines may have the same <em data-effect=\"italics\">y<\/em>-intercepts.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596557450\" data-type=\"problem\">\n<p id=\"fs-id1169596557452\">Use slopes to determine if the lines, \\(y=-5x-4\\) and \\(x-5y=5\\) are perpendicular.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596360728\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-528\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>The first equation is already in slope-intercept form.<\/td>\n<td>\\( y = -5x-4\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Solve the second equation for \\(y\\).<\/td>\n<td>\\(\\begin{array}{rcl} x-5y&amp; = &amp; 5 \\\\\u00a0 -5y&amp; = &amp;-x+5 \\\\\u00a0 \\dfrac{-5y}{-5}&amp; = &amp; \\dfrac{-x+5}{-5} \\\\\u00a0 y&amp; = &amp; \\dfrac{1}{5}x-1 \\end{array}\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Identify the slope of each line.<\/td>\n<td>\\(\\begin{array}{rcl} y&amp; = &amp; -5x-4 \\\\\u00a0 y&amp; = &amp; mx+b \\\\\u00a0 {m}_{1}&amp; = &amp; -5 \\end{array}\\)<\/td>\n<td>\\(\\begin{array}{rcl} y&amp; =&amp; \\dfrac{1}{5}x-1 \\\\\u00a0 y&amp; = &amp; mx+b \\\\\u00a0 {m}_{2}&amp; = &amp; \\dfrac{1}{5} \\end{array}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594239596\">The slopes are negative reciprocals of each other, so the lines are perpendicular. We check by multiplying the slopes,<\/p>\n\\(\\begin{array}{c}{m}_{1}\\cdot {m}_{2} \\\\ \\\\ -5\\left(\\dfrac{1}{5}\\right)\\hfill \\\\ -1\\checkmark \\hfill \\end{array}\\)\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596498259\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596379746\" data-type=\"exercise\">\n<div id=\"fs-id1169596379748\" data-type=\"problem\">\n<p id=\"fs-id1169596379750\">Use slopes to determine if the lines \\(y=-3x+2\\) and \\(x-3y=4\\) are perpendicular.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596379786\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596379788\">perpendicular<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596636409\" data-type=\"problem\">\n<p id=\"fs-id1169596636411\">Use slopes to determine if the lines \\(y=2x-5\\) and \\(x+2y=-6\\) are perpendicular.<\/p>\n\n<\/div>\n<div id=\"fs-id1169594138057\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594138060\">perpendicular<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596636403\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596636407\" data-type=\"exercise\">\n<div id=\"fs-id1169594138057\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 17<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594138070\" data-type=\"problem\">\n<p id=\"fs-id1169594138072\">Use slopes to determine if the lines, \\(7x+2y=3\\) and \\(2x+7y=5\\) are perpendicular.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596453923\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-682\" summary=\".\">\n<tbody>\n<tr>\n<td>Solve the equations for \\(y\\).<\/td>\n<td>\\(\\begin{array}{rcl}7x+2y&amp; = &amp; 3\u00a0 \\\\ 2y&amp; = &amp; -7x+3 \\\\\u00a0 \\dfrac{2y}{2}&amp; = &amp; \\dfrac{-7x+3}{2} \\\\ y&amp; = &amp; -\\dfrac{7}{2}x+\\dfrac{3}{2} \\end{array}\\)<\/td>\n<td>\\(\\begin{array}{rcl} 2x+7y&amp; = &amp; 5 \\\\\u00a0 7y&amp; = &amp; -2x+5 \\\\ \\dfrac{7y}{7}&amp; = &amp; \\dfrac{-2x+5}{7} \\\\\u00a0 y&amp; = &amp; -\\dfrac{2}{7}x+\\dfrac{5}{7} \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>Identify the slope of each line.<\/td>\n<td>\\(\\begin{array}{rcl}y&amp; = &amp; mx+b \\\\ {m}_{1}&amp; = &amp; -\\dfrac{7}{2} \\end{array}\\)<\/td>\n<td>\\(\\begin{array}{rcl} y&amp; = &amp; mx+b \\\\\u00a0{m}_{2}&amp; = &amp; -\\dfrac{2}{7} \\end{array}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"eip-901\">The slopes are reciprocals of each other, but they have the same sign. Since they are not negative reciprocals, the lines are not perpendicular.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596446075\" data-type=\"exercise\">\n<div id=\"fs-id1169596446077\" data-type=\"problem\">\n<p id=\"fs-id1169596446079\">Use slopes to determine if the lines \\(5x+4y=1\\) and \\(4x+5y=3\\) are perpendicular.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596446120\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596446122\">not perpendicular<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596548041\" data-type=\"problem\">\n<p id=\"fs-id1169596548043\">Use slopes to determine if the lines \\(2x-9y=3\\) and \\(9x-2y=1\\) are perpendicular.<\/p>\n\n<\/div>\n<div id=\"fs-id1169594236075\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594236077\">not perpendicular<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594236084\" class=\"media-2\" data-type=\"note\">\n<p id=\"fs-id1169594236088\">Access this online resource for additional instruction and practice with graphs.<\/p>\n\n<ul id=\"fs-id1169594236091\" data-display=\"block\">\n \t<li><a href=\"https:\/\/openstax.org\/l\/25GraphPractice\">Explore the Relation Between a Graph and the Slope\u2013Intercept Form of an Equation of a Line<\/a><\/li>\n<\/ul>\n<\/div>\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"fs-id1169594137963\" data-bullet-style=\"bullet\">\n \t<li><strong>The slope\u2013intercept form of an equation of a line with slope<\/strong> \\(m\\) and <em data-effect=\"italics\">y<\/em>-intercept, \\(\\left(0,b\\right)\\) is, \\(y=mx+b\\).<\/li>\n \t<li><strong data-effect=\"bold\">Graph a Line Using its Slope and <em data-effect=\"italics\">y<\/em>-Intercept<\/strong>\n<ol id=\"fs-id1169596457899\" class=\"stepwise\" type=\"1\">\n \t<li>Find the slope-intercept form of the equation of the line.<\/li>\n \t<li>Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/li>\n \t<li>Plot the <em data-effect=\"italics\">y<\/em>-intercept.<\/li>\n \t<li>Use the slope formula \\(m=\\dfrac{\\text{rise}}{\\text{run}}\\) to identify the rise and the run.<\/li>\n \t<li>Starting at the <em data-effect=\"italics\">y<\/em>-intercept, count out the rise and run to mark the second point.<\/li>\n \t<li>Connect the points with a line.<\/li>\n<\/ol>\n<\/li>\n \t<li><strong data-effect=\"bold\">Strategy for Choosing the Most Convenient Method to Graph a Line:<\/strong> Consider the form of the equation.\n<ul id=\"fs-id1169596654511\" data-bullet-style=\"open-circle\">\n \t<li>If it only has one variable, it is a vertical or horizontal line.\n\\(x=a\\) is a vertical line passing through the <em data-effect=\"italics\">x<\/em>-axis at \\(a\\).\n\\(y=b\\) is a horizontal line passing through the <em data-effect=\"italics\">y<\/em>-axis at \\(b\\).<\/li>\n \t<li>If \\(y\\) is isolated on one side of the equation, in the form \\(y=mx+b\\), graph by using the slope and <em data-effect=\"italics\">y<\/em>-intercept.\nIdentify the slope and <em data-effect=\"italics\">y<\/em>-intercept and then graph.<\/li>\n \t<li>If the equation is of the form \\(Ax+By=C\\), find the intercepts.\nFind the <em data-effect=\"italics\">x<\/em>- and <em data-effect=\"italics\">y<\/em>-intercepts, a third point, and then graph.<\/li>\n<\/ul>\n<\/li>\n \t<li><strong>Parallel lines are lines in the same plane that do not intersect.<\/strong>\n<ul id=\"fs-id1169594137035\" data-bullet-style=\"open-circle\">\n \t<li>Parallel lines have the same slope and different <em data-effect=\"italics\">y<\/em>-intercepts.<\/li>\n \t<li>If <em data-effect=\"italics\">m<\/em><sub>1<\/sub> and <em data-effect=\"italics\">m<\/em><sub>2<\/sub> are the slopes of two parallel lines then \\({m}_{1}={m}_{2}\\).<\/li>\n \t<li>Parallel vertical lines have different <em data-effect=\"italics\">x<\/em>-intercepts.<\/li>\n<\/ul>\n<\/li>\n \t<li><strong>Perpendicular lines are lines in the same plane that form a right angle.<\/strong>\n<ul id=\"fs-id1169594154465\" data-bullet-style=\"open-circle\">\n \t<li>If \\({m}_{1}\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}{m}_{2}\\) are the slopes of two perpendicular lines, then \\({m}_{1}\\cdot {m}_{2}=-1\\) and \\({m}_{1}=\\dfrac{-1}{{m}_{2}}\\).<\/li>\n \t<li>Vertical lines and horizontal lines are always perpendicular to each other.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h1 data-type=\"title\">Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1169594168892\">\n \t<dt>parallel lines<\/dt>\n \t<dd id=\"fs-id1169594168896\">Lines in the same plane that do not intersect.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594168900\">\n \t<dt>perpendicular lines<\/dt>\n \t<dd id=\"fs-id1169594168905\">Lines in the same plane that form a right angle.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594168910\">\n \t<dt>slope-intercept form of an equation of a line<\/dt>\n \t<dd id=\"fs-id1169594168914\">The slope\u2013intercept form of an equation of a line with slope <img class=\"ql-img-inline-formula quicklatex-auto-format\" title=\"Rendered by QuickLaTeX.com\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c87c998129133199e3b4192e87f227b5_l3.svg#fixme#fixme\" alt=\"m\" width=\"15\" height=\"8\"> and <em data-effect=\"italics\">y<\/em>-intercept, <img class=\"ql-img-inline-formula quicklatex-auto-format\" title=\"Rendered by QuickLaTeX.com\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-7e0694338984ab8cffa0b091f76597ea_l3.svg#fixme#fixme\" alt=\"\\left(0,b\\right)\" width=\"37\" height=\"18\"> is, <img class=\"ql-img-inline-formula quicklatex-auto-format\" title=\"Rendered by QuickLaTeX.com\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-7a6e90cb6018a244ec5be6b51fc02aef_l3.svg#fixme#fixme\" alt=\"y=mx+b\" width=\"88\" height=\"17\">.<\/dd>\n<\/dl>\n<\/div>\n<h1 data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1169594078639\">Recognize the Relation Between the Graph and the Slope\u2013Intercept Form of an Equation of a Line<\/h2>\n<p id=\"fs-id1169594078646\">In the following exercises, use the graph to find the slope and y-intercept of each line. Compare the values to the equation \\(y=mx+b\\).<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 1293px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 398px;\">\n<td style=\"width: 49.9086%; height: 398px;\"><span id=\"fs-id1169596445768\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1,2).\">1.<\/span>\n\n<span id=\"fs-id1169596445768\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1,2).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_202_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1,2).\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596445781\">\\(y=4x-2\\)<\/p>\n<\/td>\n<td style=\"width: 50.0914%; height: 398px;\"><span id=\"fs-id1169594078670\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 5) and (1, negative 2).\">2.<\/span>\n\n<span id=\"fs-id1169594078670\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 5) and (1, negative 2).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_201_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 5) and (1, negative 2).\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169594262852\">\\(y=3x-5\\)<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 398px;\">\n<td style=\"width: 49.9086%; height: 398px;\"><span id=\"fs-id1169596649110\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (1, negative 2).\">3.<\/span>\n\n<span id=\"fs-id1169596649110\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (1, negative 2).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_204_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (1, negative 2).\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596445922\">\\(y=-3x+1\\)<\/p>\n<\/td>\n<td style=\"width: 50.0914%; height: 398px;\"><span id=\"fs-id1169594008239\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,4) and (1,3).\">4.<\/span>\n\n<span id=\"fs-id1169594008239\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,4) and (1,3).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_203_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,4) and (1,3).\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169594008252\">\\(y=-x+4\\)<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 481px;\">\n<td style=\"width: 49.9086%; height: 481px;\"><span id=\"fs-id1169596541210\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,3) and (1,5).\">5.<\/span>\n\n<span id=\"fs-id1169596541210\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,3) and (1,5).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_206_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,3) and (1,5).\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596541223\">\\(y=-\\dfrac{2}{5}x+3\\)<\/p>\n<\/td>\n<td style=\"width: 50.0914%; height: 481px;\"><span id=\"fs-id1169594137785\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 3).\">6.<\/span>\n\n<span id=\"fs-id1169594137785\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 3).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_205_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 3).\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169594137798\">\\(y=-\\dfrac{4}{3}x+1\\)<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596639992\">Identify the Slope and y-Intercept From an Equation of a Line<\/h2>\n<p id=\"fs-id1169596639999\">In the following exercises, identify the slope and y-intercept of each line.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 49.9086%;\">7. \\(y=-9x+7\\)<\/td>\n<td style=\"width: 50.0914%;\">8. \\(y=-7x+3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">9. \\(y=4x-10\\)<\/td>\n<td style=\"width: 50.0914%;\">10.\\(y=6x-8\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">11. \\(4x+y=8\\)<\/td>\n<td style=\"width: 50.0914%;\">12. \\(3x+y=5\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">13. \\(8x+3y=12\\)<\/td>\n<td style=\"width: 50.0914%;\">14. \\(6x+4y=12\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">15. \\(7x-3y=9\\)<\/td>\n<td style=\"width: 50.0914%;\">16. \\(5x-2y=6\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169594240518\">Graph a Line Using Its Slope and Intercept<\/h2>\n<p id=\"fs-id1169594240524\">In the following exercises, graph the line of each equation using its slope and y-intercept.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 49.9086%;\">17. \\(y=x+4\\)<\/td>\n<td style=\"width: 50.0914%;\">18. \\(y=x+3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">19. \\(y=2x-3\\)<\/td>\n<td style=\"width: 50.0914%;\">20. \\(y=3x-1\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">21. \\(y=-x+3\\)<\/td>\n<td style=\"width: 50.0914%;\">22. \\(y=-x+2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">23. \\(y=-x-2\\)<\/td>\n<td style=\"width: 50.0914%;\">24. \\(y=-x-4\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">25. \\(y=-\\dfrac{2}{5}-3\\)<\/td>\n<td style=\"width: 50.0914%;\">26. \\(y=-\\dfrac{3}{4}-1\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">27. \\(y=-\\dfrac{2}{3}+1\\)<\/td>\n<td style=\"width: 50.0914%;\">28. \\(y=-\\dfrac{3}{5}+2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">29. \\(4x-3y=6\\)<\/td>\n<td style=\"width: 50.0914%;\">30. \\(3x-4y=8\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">31. \\(y=0.1x+15\\)<\/td>\n<td style=\"width: 50.0914%;\">32. \\(y=0.1x+15\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596394458\">Choose the Most Convenient Method to Graph a Line<\/h2>\n<p id=\"fs-id1169596394464\">In the following exercises, determine the most convenient method to graph each line.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 51.0055%;\">33. \\(y=4\\)<\/td>\n<td style=\"width: 48.9945%;\">34. \\(x=2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.0055%;\">35. \\(x=-3\\)<\/td>\n<td style=\"width: 48.9945%;\">36. \\(y=5\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.0055%;\">37. \\(y=-3x+4\\)<\/td>\n<td style=\"width: 48.9945%;\">38. \\(y=-3x+4\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.0055%;\">39. \\(x-y=1\\)<\/td>\n<td style=\"width: 48.9945%;\">40. \\(x-y=5\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.0055%;\">41. \\(y=\\dfrac{4}{5}x-3\\)<\/td>\n<td style=\"width: 48.9945%;\">42. \\(y=\\dfrac{2}{3}x-1\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.0055%;\">43. \\(y=-1\\)<\/td>\n<td style=\"width: 48.9945%;\">44. \\(y=-3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.0055%;\">45. \\(2x-5y=-10\\)<\/td>\n<td style=\"width: 48.9945%;\">46. \\(3x-2y=-12\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.0055%;\">47. \\(y=-\\dfrac{1}{3}x+5\\)<\/td>\n<td style=\"width: 48.9945%;\">48. \\(y=-\\dfrac{1}{4}+3\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596696889\">Graph and Interpret Applications of Slope\u2013Intercept<\/h2>\n<table style=\"border-collapse: collapse; width: 100%; height: 894px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 48.0804%;\">\n<p id=\"fs-id1169594137524\">49. The equation \\(P=28+2.54w\\) models the relation between the amount of Randy\u2019s monthly water bill payment, <em data-effect=\"italics\">P<\/em>, in dollars, and the number of units of water, <em data-effect=\"italics\">w<\/em>, used.<\/p>\n\n<ol id=\"fs-id1169595115415\" class=\"circled\" type=\"a\">\n \t<li>Find the payment for a month when Randy used 0 units of water.<\/li>\n \t<li>Find the payment for a month when Randy used 15 units of water.<\/li>\n \t<li>Interpret the slope and <em data-effect=\"italics\">P<\/em>-intercept of the equation.<\/li>\n \t<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 51.9196%;\">\n<p id=\"fs-id1169596696900\">50. The equation \\(P=31+1.75w\\) models the relation between the amount of Tuyet\u2019s monthly water bill payment, <em data-effect=\"italics\">P<\/em>, in dollars, and the number of units of water, <em data-effect=\"italics\">w<\/em>, used.<\/p>\n\n<ol id=\"fs-id1169595184692\" class=\"circled\" type=\"a\">\n \t<li>Find Tuyet\u2019s payment for a month when 0 units of water are used.<\/li>\n \t<li>Find Tuyet\u2019s payment for a month when 12 units of water are used.<\/li>\n \t<li>Interpret the slope and <em data-effect=\"italics\">P<\/em>-intercept of the equation.<\/li>\n \t<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.0804%;\">\n<p id=\"fs-id1169596446176\">51. Janelle is planning to rent a car while on vacation. The equation \\(C=0.32m+15\\) models the relation between the cost in dollars, <em data-effect=\"italics\">C<\/em>, per day and the number of miles, <em data-effect=\"italics\">m<\/em>, she drives in one day.<\/p>\n\n<ol id=\"fs-id1169595585090\" class=\"circled\" type=\"a\">\n \t<li>Find the cost if Janelle drives the car 0 miles one day.<\/li>\n \t<li>Find the cost on a day when Janelle drives the car 400 miles.<\/li>\n \t<li>Interpret the slope and <em data-effect=\"italics\">C<\/em>\u2013intercept of the equation.<\/li>\n \t<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 51.9196%;\">\n<p id=\"fs-id1169596446433\">52. Bruce drives his car for his job. The equation \\(R=0.575m+42\\) models the relation between the amount in dollars, <em data-effect=\"italics\">R<\/em>, that he is reimbursed and the number of miles, <em data-effect=\"italics\">m<\/em>, he drives in one day.<\/p>\n\n<ol id=\"fs-id1169595196976\" class=\"circled\" type=\"a\">\n \t<li>Find the amount Bruce is reimbursed on a day when he drives 0 miles.<\/li>\n \t<li>Find the amount Bruce is reimbursed on a day when he drives 220 miles.<\/li>\n \t<li>Interpret the slope and <em data-effect=\"italics\">R<\/em>-intercept of the equation.<\/li>\n \t<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.0804%;\">\n<p id=\"fs-id1169596445597\">53. Patel\u2019s weekly salary includes a base pay plus commission on his sales. The equation \\(S=750+0.09c\\) models the relation between his weekly salary, <em data-effect=\"italics\">S<\/em>, in dollars and the amount of his sales, <em data-effect=\"italics\">c<\/em>, in dollars.<\/p>\n\n<ol id=\"fs-id1169595585924\" class=\"circled\" type=\"a\">\n \t<li>Find Patel\u2019s salary for a week when his sales were 0.<\/li>\n \t<li>Find Patel\u2019s salary for a week when his sales were 18,540.<\/li>\n \t<li>Interpret the slope and <em data-effect=\"italics\">S<\/em>-intercept of the equation.<\/li>\n \t<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 51.9196%;\">\n<p id=\"fs-id1169596649003\">54. Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation \\(S=400+0.15c\\) models the relation between her weekly salary, <em data-effect=\"italics\">S<\/em>, in dollars and the amount of her sales, <em data-effect=\"italics\">c<\/em>, in dollars.<\/p>\n\n<ol id=\"fs-id1169595278333\" class=\"circled\" type=\"a\">\n \t<li>Find Cherie\u2019s salary for a week when her sales were 0.<\/li>\n \t<li>Find Cherie\u2019s salary for a week when her sales were 3600.<\/li>\n \t<li>Interpret the slope and <em data-effect=\"italics\">S<\/em>\u2013intercept of the equation.<\/li>\n \t<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.0804%;\">\n<p id=\"fs-id1169594041745\">55. Margie is planning a dinner banquet. The equation \\(C=750+42g\\) models the relation between the cost in dollars, <em data-effect=\"italics\">C<\/em> of the banquet and the number of guests, <em data-effect=\"italics\">g<\/em>.<\/p>\n\n<ol id=\"fs-id1169597725768\" class=\"circled\" type=\"a\">\n \t<li>Find the cost if the number of guests is 50.<\/li>\n \t<li>Find the cost if the number of guests is 100.<\/li>\n \t<li>Interpret the slope and <em data-effect=\"italics\">C<\/em>\u2013intercept of the equation.<\/li>\n \t<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 51.9196%;\">\n<p id=\"fs-id1169596697130\">56. Costa is planning a lunch banquet. The equation \\(C=450+28g\\) models the relation between the cost in dollars, <em data-effect=\"italics\">C<\/em>, of the banquet and the number of guests, <em data-effect=\"italics\">g<\/em>.<\/p>\n\n<ol id=\"fs-id1169595584374\" class=\"circled\" type=\"a\">\n \t<li>Find the cost if the number of guests is 40.<\/li>\n \t<li>Find the cost if the number of guests is 80.<\/li>\n \t<li>Interpret the slope and <em data-effect=\"italics\">C<\/em>-intercept of the equation.<\/li>\n \t<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596636338\">Use Slopes to Identify Parallel Lines<\/h2>\n<p id=\"fs-id1169596636344\">In the following exercises, use slopes and y-intercepts to determine if the lines are parallel.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 200px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 48.4461%;\">57. \\(y=\\dfrac{2}{3}x-1;\\phantom{\\rule{0.5em}{0ex}}2x-3y=-2\\)<\/td>\n<td style=\"width: 51.3711%;\">58. \\(y=\\dfrac{3}{4}x-3;\\phantom{\\rule{0.5em}{0ex}}3x-4y=-2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">59. \\(3x-4y=-2;\\phantom{\\rule{0.5em}{0ex}}y=\\dfrac{3}{4}x-3\\phantom{\\rule{0.5em}{0ex}}\\)<\/td>\n<td style=\"width: 51.3711%;\">60. \\(2x-5y=-3;\\phantom{\\rule{0.5em}{0ex}}y=\\dfrac{2}{5}x+1\\phantom{\\rule{0.5em}{0ex}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">61. \\(6x-3y=9;\\phantom{\\rule{0.5em}{0ex}}2x-y=3\\)<\/td>\n<td style=\"width: 51.3711%;\">62. \\(2x-4y=6;\\phantom{\\rule{0.5em}{0ex}}x-2y=3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">63. \\(8x+6y=6;\\phantom{\\rule{0.5em}{0ex}}12x+9y=12\\)<\/td>\n<td style=\"width: 51.3711%;\">64. \\(4x+2y=6;\\phantom{\\rule{0.5em}{0ex}}6x+3y=3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">65. \\(x=7;\\phantom{\\rule{0.5em}{0ex}}x=-8\\)<\/td>\n<td style=\"width: 51.3711%;\">66. \\(x=5;\\phantom{\\rule{0.5em}{0ex}}x=-6\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">67. \\(x=-3;\\phantom{\\rule{0.5em}{0ex}}x=-2\\)<\/td>\n<td style=\"width: 51.3711%;\">68. \\(x=-4;\\phantom{\\rule{0.5em}{0ex}}x=-1\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">69. \\(y=5;\\phantom{\\rule{0.5em}{0ex}}y=1\\)<\/td>\n<td style=\"width: 51.3711%;\">70. \\(y=2;\\phantom{\\rule{0.5em}{0ex}}y=6\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">71. \\(y=-1;\\phantom{\\rule{0.5em}{0ex}}y=2\\)<\/td>\n<td style=\"width: 51.3711%;\">72. \\(y=-4;\\phantom{\\rule{0.5em}{0ex}}y=3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">73. \\(4x+4y=8;\\phantom{\\rule{0.5em}{0ex}}x+y=2\\)<\/td>\n<td style=\"width: 51.3711%;\">74. \\(x-y=2;\\phantom{\\rule{0.5em}{0ex}}2x-2y=4\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">75. \\(5x-2y=11;\\phantom{\\rule{0.5em}{0ex}}5x-y=7\\)<\/td>\n<td style=\"width: 51.3711%;\">76. \\(x-3y=6;\\phantom{\\rule{0.5em}{0ex}}2x-6y=12\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">77. \\(4x-8y=16;\\phantom{\\rule{0.5em}{0ex}}x-2y=4\\)<\/td>\n<td style=\"width: 51.3711%;\">78. \\(3x-6y=12;\\phantom{\\rule{0.5em}{0ex}}6x-3y=3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">79. \\(x-5y=10;\\phantom{\\rule{0.5em}{0ex}}5x-y=-10\\)<\/td>\n<td style=\"width: 51.3711%;\">80. \\(9x-3y=6;\\phantom{\\rule{0.5em}{0ex}}3x-y=2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">81. \\(9x-5y=4;\\phantom{\\rule{0.5em}{0ex}}5x+9y=-1\\)<\/td>\n<td style=\"width: 51.3711%;\">82. \\(7x-4y=8;\\phantom{\\rule{0.5em}{0ex}}4x+7y=14\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596649210\">Use Slopes to Identify Perpendicular Lines<\/h2>\n<p id=\"fs-id1169596649216\">In the following exercises, use slopes and y-intercepts to determine if the lines are perpendicular.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 49.9086%;\">83. \\(x-4y=8;4x+y=2\\)<\/td>\n<td style=\"width: 50.0914%;\">84. \\(3x-2y=8;2x+3y=6\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">85. \\(2x+3y=5;3x-2y=7\\)<\/td>\n<td style=\"width: 50.0914%;\">86. \\(2x+5y=3;5x-2y=6\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">87. \\(3x-4y=8;4x-3y=6\\)<\/td>\n<td style=\"width: 50.0914%;\">88. \\(3x-2y=1;2x-3y=2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">89. \\(2x+4y=3;6x+3y=2\\)<\/td>\n<td style=\"width: 50.0914%;\">90. \\(5x+2y=6;2x+5y=8\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">91. \\(2x-6y=4;12x+4y=9\\)<\/td>\n<td style=\"width: 50.0914%;\">92. \\(4x-2y=5;3x+6y=8\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">93. \\(8x-2y=7;3x+12y=9\\)<\/td>\n<td style=\"width: 50.0914%;\">94. \\(6x-4y=5;8x+12y=3\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 49.7258%;\">\n<p id=\"fs-id1169594045888\">95. The equation \\(n=4T-160\\) is used to estimate the number of cricket chirps, <em data-effect=\"italics\">n<\/em>, in one minute based on the temperature in degrees Fahrenheit, <em data-effect=\"italics\">T<\/em>.<\/p>\n\n<ol id=\"fs-id1169597838426\" class=\"circled\" type=\"a\">\n \t<li>Explain what the slope of the equation means.<\/li>\n \t<li>Explain what the <em data-effect=\"italics\">n<\/em>\u2013intercept of the equation means. Is this a realistic situation?<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 50.2742%;\">\n<p id=\"fs-id1169596696823\">96. The equation \\(C=\\dfrac{5}{9}F-17.8\\) can be used to convert temperatures <em data-effect=\"italics\">F<\/em>, on the Fahrenheit scale to temperatures, <em data-effect=\"italics\">C<\/em>, on the Celsius scale.<\/p>\n\n<ol id=\"fs-id1169595484565\" class=\"circled\" type=\"a\">\n \t<li>Explain what the slope of the equation means.<\/li>\n \t<li>Explain what the <em data-effect=\"italics\">C<\/em>\u2013intercept of the equation means.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">97. Why are all horizontal lines parallel?<\/td>\n<td style=\"width: 50.2742%;\">98. Explain in your own words how to decide which method to use to graph a line.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 1424px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">2. slope \\(m=4\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-2\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">3. slope \\(m=-3\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,1\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">6. slope \\(m=-\\dfrac{2}{5}\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,3\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">7. \\(-9;\\left(0,7\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">10. \\(4;\\left(0,-10\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">11. \\(-4;\\left(0,8\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">14. \\(-\\dfrac{8}{3};\\left(0,4\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">15. \\(\\dfrac{7}{3};\\left(0,-3\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 288px;\">\n<td style=\"width: 50%; height: 288px;\">18.\n\n<span id=\"fs-id1169596756240\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 4) and (1, 5).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_208_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 4) and (1, 5).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%; height: 288px;\">19.\n\n<span id=\"fs-id1169596649307\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (1, negative 1).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_210_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (1, negative 1).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 288px;\">\n<td style=\"width: 50%; height: 288px;\">22.\n\n<span id=\"fs-id1169596648488\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 3) and (1, 2).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_212_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 3) and (1, 2).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%; height: 288px;\">23.\n\n<span id=\"fs-id1169594008358\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1, negative 3).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_214_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1, negative 3).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 288px;\">\n<td style=\"width: 50%; height: 288px;\">26.\n\n<span id=\"fs-id1169596383013\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (5, negative 5).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_216_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (5, negative 5).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%; height: 288px;\">27.\n\n<span id=\"fs-id1169596516339\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 1).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_218_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 1).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 288px;\">\n<td style=\"width: 50%; height: 288px;\">30.\n\n<span id=\"fs-id1169594004625\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (3,2).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_220_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (3,2).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%; height: 288px;\">31.\n\n<span id=\"fs-id1169596529660\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 25) and (negative 50, 10).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_222_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 25) and (negative 50, 10).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">34. horizontal line<\/td>\n<td style=\"width: 50%; height: 16px;\">35. vertical line<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">38. slope\u2013intercept<\/td>\n<td style=\"width: 50%; height: 16px;\">39. intercepts<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">42. slope\u2013intercept<\/td>\n<td style=\"width: 50%; height: 16px;\">43. horizontal line<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">46. intercepts<\/td>\n<td style=\"width: 50%; height: 16px;\">47. slope\u2013intercept<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">50.\n<div id=\"fs-id1169594137574\" data-type=\"solution\">\n\na) \\$28\n\nb) \\$66.10\n\nc) The slope, 2.54, means that Randy\u2019s payment, <em data-effect=\"italics\">P<\/em>, increases by \\$2.54 when the number of units of water he used, <em data-effect=\"italics\">w,<\/em> increases by 1. The <em data-effect=\"italics\">P<\/em>\u2013intercept means that if the number units of water Randy used was 0, the payment would be \\$28.\n\nd)\n<span id=\"fs-id1169596446413\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 2 to 20. The y-axis of the plane represents the variable P and runs from negative 1 to 100. The line begins at the point (0, 28) and goes through the point (15, 66.1).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_224_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 2 to 20. The y-axis of the plane represents the variable P and runs from negative 1 to 100. The line begins at the point (0, 28) and goes through the point (15, 66.1).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div><\/td>\n<td style=\"width: 50%; height: 16px;\">51.\n<div id=\"fs-id1169596648954\" data-type=\"solution\">\n\na) \\$15\n\nb) \\$143\n\nc) The slope, 0.32, means that the cost, <em data-effect=\"italics\">C<\/em>, increases by \\$0.32 when the number of miles driven, <em data-effect=\"italics\">m,<\/em> increases by 1. The <em data-effect=\"italics\">C<\/em>-intercept means that if Janelle drives 0 miles one day, the cost would be \\$15.\n\nd)\n<span id=\"fs-id1169596648983\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 1 to 500. The y-axis of the plane represents the variable C and runs from negative 1 to 200. The line begins at the point (0,15) and goes through the point (400,143).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_226_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 1 to 500. The y-axis of the plane represents the variable C and runs from negative 1 to 200. The line begins at the point (0,15) and goes through the point (400,143).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">54.\n<div id=\"fs-id1169596697088\" data-type=\"solution\">\n\na) \\$750\n\nb) \\$2418.60\n\nc) The slope, 0.09, means that Patel\u2019s salary, <em data-effect=\"italics\">S<\/em>, increases by \\$0.09 for every \\$1 increase in his sales. The <em data-effect=\"italics\">S<\/em>-intercept means that when his sales are \\$0, his salary is \\$750.\n\nd)\n<span id=\"fs-id1169596697110\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 1 to 20000. The y-axis of the plane represents the variable P and runs from negative 1 to 3000. The line begins at the point (0, 750) and goes through the point (18540, 2415).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_228_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 1 to 20000. The y-axis of the plane represents the variable P and runs from negative 1 to 3000. The line begins at the point (0, 750) and goes through the point (18540, 2415).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div><\/td>\n<td style=\"width: 50%; height: 16px;\">55.\n<div id=\"fs-id1169596636299\" data-type=\"solution\">\n\na) \\$2850\n\nb) \\$4950\n\nc) The slope, 42, means that the cost, <em data-effect=\"italics\">C<\/em>, increases by \\$42 for when the number of guests increases by 1. The <em data-effect=\"italics\">C<\/em>-intercept means that when the number of guests is 0, the cost would be \\$750.\n\nd)\n<span id=\"fs-id1169596636321\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable g and runs from negative 1 to 150. The y-axis of the plane represents the variable C and runs from negative 1 to 7000. The line begins at the point (0, 750) and goes through the point (100, 4950).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_230_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable g and runs from negative 1 to 150. The y-axis of the plane represents the variable C and runs from negative 1 to 7000. The line begins at the point (0, 750) and goes through the point (100, 4950).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">58. parallel<\/td>\n<td style=\"width: 50%; height: 16px;\">59. parallel<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">62.\u00a0parallel<\/td>\n<td style=\"width: 50%; height: 16px;\">63. parallel<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">66. parallel<\/td>\n<td style=\"width: 50%; height: 16px;\">67. parallel<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">70. parallel<\/td>\n<td style=\"width: 50%; height: 16px;\">71. parallel<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">74. not parallel<\/td>\n<td style=\"width: 50%; height: 16px;\">75. not parallel<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">78. not parallel<\/td>\n<td style=\"width: 50%; height: 16px;\">79. not parallel<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">82. not parallel<\/td>\n<td style=\"width: 50%; height: 16px;\">83. perpendicular<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">86. perpendicular<\/td>\n<td style=\"width: 50%;\">87. not perpendicular<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">90. not perpendicular<\/td>\n<td style=\"width: 50%;\">91. perpendicular<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">94. perpendicular<\/td>\n<td style=\"width: 50%;\">95.\n\na) For every increase of one degree Fahrenheit, the number of chirps increases by four.\n<div id=\"fs-id1169594045932\" data-type=\"solution\">\n\nb) There would be \\(-160\\) chirps when the Fahrenheit temperature is \\(0\\)\u00b0. (Notice that this does not make sense; this model cannot be used for all possible temperatures.)\n\n<\/div><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">98. Answers will vary.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50.0914%;\">1. slope \\(m=4\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-2\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">3. slope \\(m=-3\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">5. slope \\(m=-\\dfrac{2}{5}\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,3\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">7. \\(-9;\\left(0,7\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">9. \\(4;\\left(0,-10\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">11. \\(-4;\\left(0,8\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">13. \\(-\\dfrac{8}{3};\\left(0,4\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">15. \\(\\dfrac{7}{3};\\left(0,-3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">17.\n\n<span id=\"fs-id1169596756240\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 4) and (1, 5).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_208_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 4) and (1, 5).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.9086%;\">19.\n\n<span id=\"fs-id1169596649307\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (1, negative 1).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_210_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (1, negative 1).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">21.\n\n<span id=\"fs-id1169596648488\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 3) and (1, 2).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_212_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 3) and (1, 2).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.9086%;\">23.\n\n<span id=\"fs-id1169594008358\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1, negative 3).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_214_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1, negative 3).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">25.\n\n<span id=\"fs-id1169596383013\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (5, negative 5).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_216_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (5, negative 5).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.9086%;\">27.\n\n<span id=\"fs-id1169596516339\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 1).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_218_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 1).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">29.\n\n<span id=\"fs-id1169594004625\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (3,2).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_220_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (3,2).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.9086%;\">31.\n\n<span id=\"fs-id1169596529660\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 25) and (negative 50, 10).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_222_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 25) and (negative 50, 10).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">33. horizontal line<\/td>\n<td style=\"width: 49.9086%;\">35. vertical line<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">37. slope\u2013intercept<\/td>\n<td style=\"width: 49.9086%;\">39. intercepts<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">41. slope\u2013intercept<\/td>\n<td style=\"width: 49.9086%;\">43. horizontal line<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">45. intercepts<\/td>\n<td style=\"width: 49.9086%;\">47. slope\u2013intercept<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">49.\n<div id=\"fs-id1169594137574\" data-type=\"solution\">\n\na) \\$28\n\nb) \\$66.10\n\nc) The slope, 2.54, means that Randy\u2019s payment, <em data-effect=\"italics\">P<\/em>, increases by \\$2.54 when the number of units of water he used, <em data-effect=\"italics\">w,<\/em> increases by 1. The <em data-effect=\"italics\">P<\/em>\u2013intercept means that if the number units of water Randy used was 0, the payment would be \\$28.\n\nd)\n<span id=\"fs-id1169596446413\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 2 to 20. The y-axis of the plane represents the variable P and runs from negative 1 to 100. The line begins at the point (0, 28) and goes through the point (15, 66.1).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_224_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 2 to 20. The y-axis of the plane represents the variable P and runs from negative 1 to 100. The line begins at the point (0, 28) and goes through the point (15, 66.1).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div><\/td>\n<td style=\"width: 49.9086%;\">51.\n<div id=\"fs-id1169596648954\" data-type=\"solution\">\n\na) \\$15\n\nb) \\$143\n\nc) The slope, 0.32, means that the cost, <em data-effect=\"italics\">C<\/em>, increases by \\$0.32 when the number of miles driven, <em data-effect=\"italics\">m,<\/em> increases by 1. The <em data-effect=\"italics\">C<\/em>-intercept means that if Janelle drives 0 miles one day, the cost would be \\$15.\n\nd)\n<span id=\"fs-id1169596648983\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 1 to 500. The y-axis of the plane represents the variable C and runs from negative 1 to 200. The line begins at the point (0,15) and goes through the point (400,143).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_226_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 1 to 500. The y-axis of the plane represents the variable C and runs from negative 1 to 200. The line begins at the point (0,15) and goes through the point (400,143).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">53.\n<div id=\"fs-id1169596697088\" data-type=\"solution\">\n\na) \\$750\n\nb) \\$2418.60\n\nc) The slope, 0.09, means that Patel\u2019s salary, <em data-effect=\"italics\">S<\/em>, increases by \\$0.09 for every \\$1 increase in his sales. The <em data-effect=\"italics\">S<\/em>-intercept means that when his sales are \\$0, his salary is \\$750.\n\nd)\n<span id=\"fs-id1169596697110\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 1 to 20000. The y-axis of the plane represents the variable P and runs from negative 1 to 3000. The line begins at the point (0, 750) and goes through the point (18540, 2415).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_228_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 1 to 20000. The y-axis of the plane represents the variable P and runs from negative 1 to 3000. The line begins at the point (0, 750) and goes through the point (18540, 2415).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div><\/td>\n<td style=\"width: 49.9086%;\">55.\n<div id=\"fs-id1169596636299\" data-type=\"solution\">\n\na) \\$2850\n\nb) \\$4950\n\nc) The slope, 42, means that the cost, <em data-effect=\"italics\">C<\/em>, increases by \\$42 for when the number of guests increases by 1. The <em data-effect=\"italics\">C<\/em>-intercept means that when the number of guests is 0, the cost would be \\$750.\n\nd)\n<span id=\"fs-id1169596636321\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable g and runs from negative 1 to 150. The y-axis of the plane represents the variable C and runs from negative 1 to 7000. The line begins at the point (0, 750) and goes through the point (100, 4950).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_230_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable g and runs from negative 1 to 150. The y-axis of the plane represents the variable C and runs from negative 1 to 7000. The line begins at the point (0, 750) and goes through the point (100, 4950).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">57. parallel<\/td>\n<td style=\"width: 49.9086%;\">59. parallel<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">61. parallel<\/td>\n<td style=\"width: 49.9086%;\">63. parallel<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">65. parallel<\/td>\n<td style=\"width: 49.9086%;\">67. parallel<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">69. parallel<\/td>\n<td style=\"width: 49.9086%;\">71. parallel<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">73. not parallel<\/td>\n<td style=\"width: 49.9086%;\">75. not parallel<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">77. not parallel<\/td>\n<td style=\"width: 49.9086%;\">79. not parallel<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">81. not parallel<\/td>\n<td style=\"width: 49.9086%;\">83. perpendicular<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">85. perpendicular<\/td>\n<td style=\"width: 49.9086%;\">87. not perpendicular<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">89. not perpendicular<\/td>\n<td style=\"width: 49.9086%;\">91. perpendicular<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">93. perpendicular<\/td>\n<td style=\"width: 49.9086%;\">95.\n\na) For every increase of one degree Fahrenheit, the number of chirps increases by four.\n<div id=\"fs-id1169594045932\" data-type=\"solution\">\n\nb) There would be \\(-160\\) chirps when the Fahrenheit temperature is \\(0\\)\u00b0. (Notice that this does not make sense; this model cannot be used for all possible temperatures.)\n\n<\/div><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">97. Answers will vary.<\/td>\n<td style=\"width: 49.9086%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cUse the Slope\u2013Intercept Form of an Equation of a Line\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Recognize the relation between the graph and the slope\u2013intercept form of an equation of a line<\/li>\n<li>Identify the slope and y-intercept form of an equation of a line<\/li>\n<li>Graph a line using its slope and intercept<\/li>\n<li>Choose the most convenient method to graph a line<\/li>\n<li>Graph and interpret applications of slope\u2013intercept<\/li>\n<li>Use slopes to identify parallel lines<\/li>\n<li>Use slopes to identify perpendicular lines<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Recognize the Relation Between the Graph and the Slope\u2013Intercept Form of an Equation of a Line<\/h1>\n<p id=\"fs-id1169596251841\">We have graphed linear equations by plotting points, using intercepts, recognizing horizontal and vertical lines, and using the point\u2013slope method. Once we see how an equation in slope\u2013intercept form and its graph are related, we\u2019ll have one more method we can use to graph lines.<\/p>\n<p id=\"fs-id1169594172366\">In <a href=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebra1editing\/chapter\/graph-linear-equations-in-two-variables\/\">Graph Linear Equations in Two Variables<\/a>, we graphed the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fe4c81cc2a658e51ba14155245da8746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\" \/> by plotting points. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_05_001\">(Figure)<\/a>. Let\u2019s find the slope of this line.<\/p>\n<div id=\"CNX_ElemAlg_Figure_04_05_001\" class=\"bc-figure figure\"><span id=\"fs-id1169594050718\" data-type=\"media\" data-alt=\"This figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The line is labeled with the equation y equals one half x, plus 3. The points (0, 3), (2, 4) and (4, 5) are labeled also. A red vertical line begins at the point (2, 4) and ends one unit above the point. It is labeled \u201cRise equals 1\u201d. A red horizontal line begins at the end of the vertical line and ends at the point (4, 5). It is labeled \u201cRun equals 2. The red lines create a right triangle with the line y equals one half x, plus 3 as the hypotenuse.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/07\/CNX_ElemAlg_Figure_04_05_001_img_new.jpg\" alt=\"This figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The line is labeled with the equation y equals one half x, plus 3. The points (0, 3), (2, 4) and (4, 5) are labeled also. A red vertical line begins at the point (2, 4) and ends one unit above the point. It is labeled \u201cRise equals 1\u201d. A red horizontal line begins at the end of the vertical line and ends at the point (4, 5). It is labeled \u201cRun equals 2. The red lines create a right triangle with the line y equals one half x, plus 3 as the hypotenuse.\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<p id=\"fs-id1169596237835\">The red lines show us the rise is 1 and the run is 2. Substituting into the slope formula:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2c1fa682c96e8a5ced90e703ca82ab3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#109;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#105;&#115;&#101;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#117;&#110;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#109;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"71\" width=\"91\" style=\"vertical-align: -31px;\" \/><\/p>\n<p id=\"fs-id1169594206666\">What is the <em data-effect=\"italics\">y<\/em>-intercept of the line? The <em data-effect=\"italics\">y<\/em>-intercept is where the line crosses the <em data-effect=\"italics\">y<\/em>-axis, so <em data-effect=\"italics\">y<\/em>-intercept is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef24d382319a3ce81f280194edba003a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>. The equation of this line is:<\/p>\n<p><span id=\"fs-id1169596364667\" data-type=\"media\" data-alt=\"The figure shows the equation y equals one half x, plus 3. The fraction one half is colored red and the number 3 is colored blue.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_034_img_new.jpg\" alt=\"The figure shows the equation y equals one half x, plus 3. The fraction one half is colored red and the number 3 is colored blue.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169594159235\">Notice, the line has:<\/p>\n<p><span id=\"fs-id1169596696275\" data-type=\"media\" data-alt=\"The figure shows the statement \u201cslope m equals one half and y-intercept (0, 3). The slope, one half, is colored red and the number 3 in the y-intercept is colored blue.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_035_img_new.jpg\" alt=\"The figure shows the statement \u201cslope m equals one half and y-intercept (0, 3). The slope, one half, is colored red and the number 3 in the y-intercept is colored blue.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596404951\">When a linear equation is solved for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>, the coefficient of the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> term is the slope and the constant term is the <em data-effect=\"italics\">y<\/em>-coordinate of the <em data-effect=\"italics\">y<\/em>-intercept. We say that the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fe4c81cc2a658e51ba14155245da8746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\" \/> is in slope\u2013intercept form.<\/p>\n<p><span id=\"fs-id1169596219400\" data-type=\"media\" data-alt=\"The figure shows the statement \u201cm equals one half; y-intercept is (0, 3). The slope, one half, is colored red and the number 3 in the y-intercept is colored blue. Below that statement is the equation y equals one half x, plus 3. The fraction one half is colored red and the number 3 is colored blue. Below the equation is another equation y equals m x, plus b. The variable m is colored red and the variable b is colored blue.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_015_img_new.jpg\" alt=\"The figure shows the statement \u201cm equals one half; y-intercept is (0, 3). The slope, one half, is colored red and the number 3 in the y-intercept is colored blue. Below that statement is the equation y equals one half x, plus 3. The fraction one half is colored red and the number 3 is colored blue. Below the equation is another equation y equals m x, plus b. The variable m is colored red and the variable b is colored blue.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div id=\"fs-id1169596318095\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Slope-intercept form of an equation of a line<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596311488\">The slope\u2013intercept form of an equation of a line with slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-05dbabd42fe84ba97e673be0628c5974_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"37\" style=\"vertical-align: -4px;\" \/> is,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p>Sometimes the slope\u2013intercept form is called the \u201c<em>y<\/em>-form.\u201d<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594028925\" data-type=\"problem\">\n<p id=\"fs-id1169596698756\">Use the graph to find the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8af503cd473a72e30e30c2d46c7575ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p id=\"fs-id1169596285072\">Compare these values to the equation<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594011994\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596654281\">To find the slope of the line, we need to choose two points on the line. We\u2019ll use the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-99d11505e9b59f8e2d3351529e3354c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-450ee1faefebebc715b20a97daae94ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<table id=\"eip-id1172185589908\" class=\"unnumbered unstyled can-break\" summary=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The line is labeled with the equation y equals 2 x, plus 1. The points (negative 2, negative 3), (0, 1) and (1, 3) are plotted. Below the graph are the steps to find the slope of the line. Step 1 is the find the rise and run. The equation for slope is m equals rise divided by run. The rise is 2 and the run is 1. The slope equation becomes 2 divided by 1 which is 2. Step 2 is the find the y-intercept of the line. The y-intercept is the point (0, 1). In step 3 we compare the values found to the equation. Show in this step is the statement \u201cWe found slope m equals 2 and y-intercept is (0, 1)\u201d. The slope, 2, is colored red and the number 1 in the y-intercept is colored blue. The equation y equals 2 x, plus 3. In the equation the number 2 is colored red and the number 1 is colored blue. Below the equation is another equation y equals m x, plus b. The variable m is colored red and the variable b is colored blue.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><span id=\"eip-id1172186758147\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_016b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find the rise and run.<\/td>\n<td><span id=\"eip-id1172180058520\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_016c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187650033\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_016d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187401821\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_016e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find the <em data-effect=\"italics\">y<\/em>-intercept of the line.<\/td>\n<td data-align=\"center\">The <em data-effect=\"italics\">y<\/em>-intercept is the point (0, 1).<\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1172189015101\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_016a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1172185602140\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_016f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596656286\">The slope is the same as the coefficient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and the <em data-effect=\"italics\">y<\/em>-coordinate of the <em data-effect=\"italics\">y<\/em>-intercept is the same as the constant term.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596292085\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594001998\" data-type=\"exercise\">\n<div id=\"fs-id1169596459717\" data-type=\"problem\">\n<p id=\"fs-id1169596382613\">Use the graph to find the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-56977bb9bf99835acf4e5c84148ac24d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/>. Compare these values to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><span id=\"fs-id1169596232523\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The line goes through the points (0, negative 1) and (6, 3).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_018_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The line goes through the points (0, negative 1) and (6, 3).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id1169596687837\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596240719\">slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5739129da8f1e985b237b54505899cc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"50\" style=\"vertical-align: -12px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec6084fa217f87f8fc5df481ca60ccf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596235127\" data-type=\"problem\">\n<p id=\"fs-id1169596395779\">Use the graph to find the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fe4c81cc2a658e51ba14155245da8746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\" \/>. Compare these values to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><span id=\"fs-id1169596292349\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The line goes through the points (0, 3) and (negative 6, 0).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_019_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The line goes through the points (0, 3) and (negative 6, 0).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id1169596365028\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596589952\">slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ef41f038f64d1359e49d5ea433122d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"50\" style=\"vertical-align: -12px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef24d382319a3ce81f280194edba003a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Identify the Slope and <em data-effect=\"italics\">y<\/em>-Intercept From an Equation of a Line<\/h1>\n<p id=\"fs-id1169596620860\">In <a class=\"target-chapter\" href=\"\/contents\/ba42b46c-de39-4f91-a515-06bfd7a16c6b\">Understand Slope of a Line<\/a>, we graphed a line using the slope and a point. When we are given an equation in slope\u2013intercept form, we can use the <em data-effect=\"italics\">y<\/em>-intercept as the point, and then count out the slope from there. Let\u2019s practice finding the values of the slope and <em data-effect=\"italics\">y<\/em>-intercept from the equation of a line.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596551201\" data-type=\"problem\">\n<p id=\"fs-id1169596590337\">Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line with equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9ca7e6824e1b3783daf117b3e7f97530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"95\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596530050\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596655608\">We compare our equation to the slope\u2013intercept form of the equation.<\/p>\n<table id=\"eip-id1172183346253\" class=\"unnumbered unstyled can-break\" style=\"width: 425px;\" summary=\"This figure has two columns. At the top of the figure, the left column says \u201cStep 1. Write the slope-intercept form of the equation of the line.\u201d The right column contains y equals mx plus b, with the variable m written in red and the variable b written in blue. One row down, the left column says \u201cStep 2. Write the equation of the line. The right column contains y equals negative 3x plus 5. Negative 3 is written in red and 5 is written in blue. One row down, the left column says \u201cStep 3. Identify the slope.\u201d The right column contains m equals negative 3. One row down, the left column says \u201cStep 4. Identify the y-intercept.\u201d The right column contains says \u201cy-intercept is (0, 5).\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 184.406px;\"><\/td>\n<td style=\"width: 211.406px;\"><span id=\"eip-id1172188022250\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_020a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 184.406px;\">Write the equation of the line.<\/td>\n<td style=\"width: 211.406px;\"><span id=\"eip-id1172187806518\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_020b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 184.406px;\">Identify the slope.<\/td>\n<td style=\"width: 211.406px;\"><span id=\"eip-id1172187837003\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_020c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 184.406px;\">Identify the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td style=\"width: 211.406px;\"><span id=\"eip-id1172184396691\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_020d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596276598\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596379858\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169594080569\">Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aa4adf762af244c419f3616777f2926c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596457078\" data-type=\"solution\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66991e6486078b80f527ab5b1757c9ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"71\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596380932\" data-type=\"problem\">\n<p id=\"fs-id1169596303982\">Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2e1ed76d5373469bd2126fe9167b65aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"99\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596685210\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596591237\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-156052e2a84facb16efb961337655677_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"72\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>When an equation of a line is not given in slope\u2013intercept form, our first step will be to solve the equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596299435\" data-type=\"problem\">\n<p id=\"fs-id1169596363327\">Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line with equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-57266acf353f74b1688f614aa9924f89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596310364\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596387390\">This equation is not in slope\u2013intercept form. In order to compare it to the slope\u2013intercept form we must first solve the equation for<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<table id=\"eip-id1172187679758\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the left column says \u201cSolve for y.\u201d The right column contains the equation x plus 2y equals 6. One row down, the text in the left column says \u201cSubtract x from each side.\u201d The right column contains 2y equals negative x plus 6. One row down, the text in the left column says \u201cDivide both sides by 2.\u201d The right column contains 2y divided by 2 equals negative x plus 6 divided by 2. One row down, the text on the left says \u201cSimplify. Remember: a plus b divided by c equals a divided by c plus b divided by c.\u201d The right column contains 2y divided by 2 equals negative x divided by 2 plus 6 divided by 2. One row down, the text on the left says \u201cSimplify.\u201d The right column contains y equals negative 1 half x plus 3. One row down, the left column says \u201cWrite the slope-intercept form of the equation of the line.\u201d The right column contains y equals mx plus b, with the variable m written in red and the variable b written in blue. One row down, the text in the left column says \u201cWrite the equation of the line.\u201d The right column contains y equals negative 1 half x plus 3. Negative 1 half is written in red and 3 is written in blue. One row down, the left column says \u201cIdentify the slope.\u201d The right column contains m equals negative 1 half. One row down, the left column says \u201cIdentify the y-intercept.\u201d The right column contains says \u201cy-intercept is (0, 3).\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Solve for <em data-effect=\"italics\">y<\/em>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-57266acf353f74b1688f614aa9924f89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract <em data-effect=\"italics\">x<\/em> from each side.<\/td>\n<td><span id=\"eip-id1172187196124\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 2.<\/td>\n<td><span id=\"eip-id1172187110656\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172187600506\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>(Remember:<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-83f34b17f0ec09079fd090974e8179c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#43;&#98;&#125;&#123;&#99;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"109\" style=\"vertical-align: -12px;\" \/>)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172186748318\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the slope\u2013intercept form of the equation of the line.<\/td>\n<td><span id=\"eip-id1172186037414\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the equation of the line.<\/td>\n<td><span id=\"eip-id1172189361890\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Identify the slope.<\/td>\n<td><span id=\"fs-id1169751895483\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Identify the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td><span id=\"fs-id1169751959438\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_021h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596622645\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594075433\" data-type=\"exercise\">\n<div id=\"fs-id1169594157418\" data-type=\"problem\">\n<p id=\"fs-id1169596765660\">Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-971440700f82c87567aa141fb48186a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#52;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596366913\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-77ed718459bce47c62a2649e27e9eab6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"72\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594082663\" data-type=\"problem\">\n<p id=\"fs-id1169596516662\">Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-64c943eb082c01ef6bb9fde386b62b80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596244470\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596438180\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d40f63aebacc9a7707574f84e68b1b3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"72\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Graph a Line Using its Slope and Intercept<\/h1>\n<p id=\"fs-id1169596499436\">Now that we know how to find the slope and <em data-effect=\"italics\">y<\/em>-intercept of a line from its equation, we can graph the line by plotting the <em data-effect=\"italics\">y<\/em>-intercept and then using the slope to find another point.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How to Graph a Line Using its Slope and Intercept<\/div>\n<div id=\"fs-id1169596411988\" data-type=\"exercise\">\n<div id=\"fs-id1169596593452\" data-type=\"problem\">\n<p id=\"fs-id1169596318600\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d76269f8d9b324873c9b8e3993ef6892_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<div id=\"fs-id1169594160299\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p><span id=\"fs-id1169594053951\" data-type=\"media\" data-alt=\"The figure shows the steps to graph the equation y equals 4x minus 2. Step 1 is to find the slope intercept form of the equation. The equation is already in slope intercept form.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_033a_img_new.jpg\" alt=\"The figure shows the steps to graph the equation y equals 4x minus 2. Step 1 is to find the slope intercept form of the equation. The equation is already in slope intercept form.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169594053625\" data-type=\"media\" data-alt=\"Step 2 is to identify the slope and y-intercept. Use the equation y equals m x, plus b. The equation y equals m x, plus b is shown with the variable m colored red and the variable b colored blue. Below that is the equation y equals 4 x, plus -2. The number 4 is colored red and -2 is colored blue. From this equation we can see that m equals 4 and b equals -2 so the slope is 4 and the y-intercept is the point (0, negative 2).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_033b_img_new.jpg\" alt=\"Step 2 is to identify the slope and y-intercept. Use the equation y equals m x, plus b. The equation y equals m x, plus b is shown with the variable m colored red and the variable b colored blue. Below that is the equation y equals 4 x, plus -2. The number 4 is colored red and -2 is colored blue. From this equation we can see that m equals 4 and b equals -2 so the slope is 4 and the y-intercept is the point (0, negative 2).\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596285435\" data-type=\"media\" data-alt=\"Step 3 is to plot the y-intercept. An x y-coordinate plane is shown with the x-axis of the plane running from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The point (0, negative 2) is plotted.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_033c_img_new.jpg\" alt=\"Step 3 is to plot the y-intercept. An x y-coordinate plane is shown with the x-axis of the plane running from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The point (0, negative 2) is plotted.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169594086346\" data-type=\"media\" data-alt=\"Step 4 is to use the slope formula m equals rise over run to identify the rise and the run. Since m equals 4, rise over run equals 4 over 1. From this we can determine that the rise is 4 and the run is 1.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_033d_img_new.jpg\" alt=\"Step 4 is to use the slope formula m equals rise over run to identify the rise and the run. Since m equals 4, rise over run equals 4 over 1. From this we can determine that the rise is 4 and the run is 1.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596381128\" data-type=\"media\" data-alt=\"Step 5 is to start at they-intercept, count out the rise and run to mark the second point. So start at the point (0, negative 2) and count the rise and the run. The rise is up 4 and the run is right 1. On the x y-coordinate plane is a red vertical line starts at the point (0, negative 2) and rises 4 units at its end a red horizontal line runs 1 unit to end at the point (1, 2). The point (1, 2) is plotted.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_033e_img_new.jpg\" alt=\"Step 5 is to start at they-intercept, count out the rise and run to mark the second point. So start at the point (0, negative 2) and count the rise and the run. The rise is up 4 and the run is right 1. On the x y-coordinate plane is a red vertical line starts at the point (0, negative 2) and rises 4 units at its end a red horizontal line runs 1 unit to end at the point (1, 2). The point (1, 2) is plotted.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596662513\" data-type=\"media\" data-alt=\"Step 6 is to connect the points with a line. On the x y-coordinate plane the points (0, negative 2) and (1, 2) are plotted and a line runs through the two points. The line is the graph of y equals 4 x, minus 2.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_033f_img_new.jpg\" alt=\"Step 6 is to connect the points with a line. On the x y-coordinate plane the points (0, negative 2) and (1, 2) are plotted and a line runs through the two points. The line is the graph of y equals 4 x, minus 2.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596369784\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596706450\" data-type=\"exercise\">\n<div id=\"fs-id1169596446736\" data-type=\"problem\">\n<p id=\"fs-id1169594031888\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f8c64714e59a156d66b03d612d2a0f36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596236687\" data-type=\"solution\"><span id=\"fs-id1169596404554\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, 1) and (1, 5) are plotted on the line.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_002_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, 1) and (1, 5) are plotted on the line.\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594149466\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594029304\" data-type=\"exercise\">\n<div id=\"fs-id1169596256256\" data-type=\"solution\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594028383\" data-type=\"problem\">\n<p id=\"fs-id1169594031441\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e09b4ae6d312635fcb8ec259a322e66d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596256256\" data-type=\"solution\"><span id=\"fs-id1169596702940\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 3) and (1, negative 1) are plotted on the line.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_003_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 3) and (1, negative 1) are plotted on the line.\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594149466\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594029304\" data-type=\"exercise\">\n<div id=\"fs-id1169596256256\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Graph a line using its slope and <em data-effect=\"italics\">y<\/em>-intercept<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169596372582\" class=\"stepwise\" type=\"1\">\n<li>Find the slope-intercept form of the equation of the line.<\/li>\n<li>Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/li>\n<li>Plot the <em data-effect=\"italics\">y<\/em>-intercept.<\/li>\n<li>Use the slope formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7bf3b27f8bf32d800686f5f7ddef6962_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#105;&#115;&#101;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#117;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"68\" style=\"vertical-align: -12px;\" \/> to identify the rise and the run.<\/li>\n<li>Starting at the <em data-effect=\"italics\">y<\/em>-intercept, count out the rise and run to mark the second point.<\/li>\n<li>Connect the points with a line.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596767304\" class=\"howto\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596656244\" data-type=\"problem\">\n<p id=\"fs-id1169596235895\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a47a249be356e3261dd0f2ebe6f9d2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -4px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<div id=\"fs-id1169594149555\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172184404871\" class=\"unnumbered unstyled can-break\" summary=\"This figure shows the steps to graph the equation y equals negative x plus 4. The first step is to put the equation in slope-intercept form. y equals negative x plus 4 is already in slope-intercept form. The second step is to identify the slope and y-intercept. The slope, m, equals negative 1, and the y intercept is (0, 4). The third step is to plot the y-intercept. The fourth step is to identify the rise and run, which is negative 1 over 1. Step 5 is to count out the rise and run to mark the second point, and step 6 is to draw the line. At the very bottom of the figure is a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The points (0, 4) and (1, 3) are plotted on the line.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>The equation is in slope\u2013intercept form.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a47a249be356e3261dd0f2ebe6f9d2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec3d084a8add5b00b06df1310c62281e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><em data-effect=\"italics\">y<\/em>-intercept is (0, 4)<\/td>\n<\/tr>\n<tr>\n<td>Plot the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td>See graph below.<\/td>\n<\/tr>\n<tr>\n<td>Identify the rise and the run.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e6bcaf0304fabc2d7dbc9aebb369841_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#49;&#125;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"64\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Count out the rise and run to mark the second point.<\/td>\n<td>rise \u22121, run 1<\/td>\n<\/tr>\n<tr>\n<td>Draw the line.<\/td>\n<td><span id=\"eip-id1172183636610\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" data-align=\"center\">To check your work, you can find another point on the line and make sure it is a solution of the equation. In the graph we see the line goes through (4, 0).<\/td>\n<\/tr>\n<tr>\n<td>Check.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0874bfaaeb840d983c1d2785f0cb48bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#125;&#32;&#121;&#32;&#61;&#45;&#120;&#43;&#52;&#32;&#92;&#92;&#32;&#32;&#48;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#45;&#52;&#43;&#52;&#32;&#92;&#92;&#32;&#32;&#48;&#32;&#61;&#32;&#48;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"88\" style=\"vertical-align: -26px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596446271\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596621546\" data-type=\"exercise\">\n<div id=\"fs-id1169596226960\" data-type=\"problem\">\n<p id=\"fs-id1169596702137\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17ca43185f82c1ced7cfbb2d59df5f69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -4px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596446052\" data-type=\"solution\"><span id=\"fs-id1169596554450\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 3) and (1, negative 4) are plotted on the line.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_005_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 3) and (1, negative 4) are plotted on the line.\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596764611\" data-type=\"problem\">\n<p id=\"fs-id1169596764574\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c68f61224271c29eab1676acf3ebb6c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596703969\" data-type=\"solution\"><span id=\"fs-id1169596379010\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 1) and (1, negative 2) are plotted on the line.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_006_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 1) and (1, negative 2) are plotted on the line.\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594001481\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596764608\" data-type=\"exercise\">\n<div id=\"fs-id1169596703969\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594010890\" data-type=\"problem\">\n<p id=\"fs-id1169594243912\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f495c68d43ebdd707e034c113d15464a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"100\" style=\"vertical-align: -12px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<div id=\"fs-id1169594029231\" data-type=\"solution\">\n<div data-type=\"title\"><strong><br \/>\nSolution<\/strong><\/div>\n<table id=\"eip-id1172187131981\" class=\"unnumbered unstyled can-break\" summary=\"This figure shows the steps to graph the equation y equals negative 2 thirds x minus 3. The first step is to put the equation in slope-intercept form. y equals negative 2 thirds x minus 3 is already in slope-intercept form. The second step is to identify the slope and y-intercept. The slope, m, equals negative 2 thirds, and the y intercept is (0, negative 3). Step 4 is to count out the rise and run to mark the second point, and step 5 is to draw the line. At the very bottom of the figure is a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The points (0, negative 3) and (3, negative 5) are plotted on the line.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>The equation is in slope\u2013intercept form.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f495c68d43ebdd707e034c113d15464a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"100\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1f73f43cc9463a5d8bd1388705e24bff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"64\" style=\"vertical-align: -12px;\" \/>; <em data-effect=\"italics\">y<\/em>-intercept is (0, \u22123)<\/td>\n<\/tr>\n<tr>\n<td>Plot the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td>See graph below.<\/td>\n<\/tr>\n<tr>\n<td>Identify the rise and the run.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Count out the rise and run to mark the second point.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Draw the line.<\/td>\n<td><span id=\"eip-id1172187684428\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596655631\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596364893\" data-type=\"exercise\">\n<div id=\"fs-id1169596364896\" data-type=\"problem\">\n<p id=\"fs-id1169594002076\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f97c369b76d40f2801ed73c5b4547333_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"99\" style=\"vertical-align: -12px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596698712\" data-type=\"solution\"><span id=\"fs-id1169596235577\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0,1) and (2, negative 4) are plotted on the line.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_008_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0,1) and (2, negative 4) are plotted on the line.\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594241409\" data-type=\"problem\">\n<p id=\"fs-id1169596435270\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-06461bee1553097a4040f0604c9d6571_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"99\" style=\"vertical-align: -12px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596648398\" data-type=\"solution\"><span id=\"fs-id1169596648402\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 2) and (4, negative 5) are plotted on the line.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_009_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 2) and (4, negative 5) are plotted on the line.\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596516694\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594241407\" data-type=\"exercise\">\n<div id=\"fs-id1169596648398\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596253295\" data-type=\"problem\">\n<p id=\"fs-id1169596253298\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-efedfb1adc9ce250cfc862e4fb07e730_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#51;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<div id=\"fs-id1169596555123\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172188103261\" class=\"unnumbered unstyled can-break\" summary=\"This figure shows the steps to graph the equation 4x minus 3y equals 12. The first step is to put the equation in slope-intercept form. Subtract 4x from both sides to get negative 3y equals negative 4x plus 12. Divide both sides by negative 3 to get y equals 4 thirds x minus 4, which is in y-intercept form. The second step is to identify the slope and y-intercept. The slope, m, equals 4 thirds, and the y intercept is (0, negative 4). Step 3 is to plot the y-intercept. Step 4 is to count out the rise and run to mark the second point, and step 5 is to draw the line. At the very bottom of the figure is a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The points (0, negative 4) and (3, 0) are plotted on the line.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-efedfb1adc9ce250cfc862e4fb07e730_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#51;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Find the slope\u2013intercept form of the equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9d2ce3f04a63690db29e1d65adfc1efd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#121;&#61;&#45;&#52;&#120;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"126\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc7d15b1a0494cae27ccc6f6577c3500_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#121;&#125;&#123;&#51;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#52;&#120;&#43;&#49;&#50;&#125;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"133\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>The equation is now in slope\u2013intercept form.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a2379e47c139d09ef54dc6a16db73fc9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70fe2977b04eb74081a54e4989b4e637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"50\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><em data-effect=\"italics\">y<\/em>-intercept is (0, \u22124)<\/td>\n<\/tr>\n<tr>\n<td>Plot the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td>See graph below.<\/td>\n<\/tr>\n<tr>\n<td>Identify the rise and the run; count out the rise and run to mark the second point.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Draw the line.<\/td>\n<td><span id=\"eip-id1172183643963\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594064448\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596348900\" data-type=\"exercise\">\n<div id=\"fs-id1169596348903\" data-type=\"problem\">\n<p id=\"fs-id1169596235492\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d0154cab020c706f037ada227e3f65b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596377717\" data-type=\"solution\"><span id=\"fs-id1169596245210\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 6) and (1, negative 4) are plotted on the line.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_011_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 6) and (1, negative 4) are plotted on the line.\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596689546\" data-type=\"problem\">\n<p id=\"fs-id1169596689548\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4876a6ef3d42a73721a021f2b3fbc92a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#50;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169594061626\" data-type=\"solution\"><span id=\"fs-id1169594061629\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 4) and (2, negative 1) are plotted on the line.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_012_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 4) and (2, negative 1) are plotted on the line.\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596403566\">We have used a grid with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> both going from about <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24329a36a4e10288288979f77a565ca2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> to 10 for all the equations we\u2019ve graphed so far. Not all linear equations can be graphed on this small grid. Often, especially in applications with real-world data, we\u2019ll need to extend the axes to bigger positive or smaller negative numbers.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596653186\" data-type=\"problem\">\n<p id=\"fs-id1169596234434\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9978bf64ff03e72a6c40a3b8dad23786_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;&#46;&#50;&#120;&#43;&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -4px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<div id=\"fs-id1169594085611\" data-type=\"solution\">\n<div data-type=\"title\"><strong><br \/>\nSolution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169594085616\">We\u2019ll use a grid with the axes going from about <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3f7920c1ff891a318599e38fe5bcd7ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> to 80.<\/p>\n<table id=\"eip-id1172183813237\" class=\"unnumbered unstyled can-break\" summary=\"This figure shows the steps to graph the equation y equals 0.2x plus 45. The first step is to put the equation in slope-intercept form. y equals 0.2x plus 45is in y-intercept form. The second step is to identify the slope and y-intercept. The slope, m, equals 0.2, and the y intercept is (0, 45). Step 3 is to plot the y-intercept. Step 4 is to count out the rise and run to mark the second point. The slope is m equals 0.2; in fraction form this means m equals 2 tenths. Given the scale of our graph, it would be easier to use the equivalent fraction m equals 10 fiftieths. Step 5 is to draw the line. At the very bottom of the figure is a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 80 to 80. The y-axis of the plane runs from negative 80 to 80. The points (0, 45) and (50, 55) are plotted on the line.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 380.406px;\"><\/td>\n<td style=\"width: 272.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 380.406px;\">The equation is in slope\u2013intercept form.<\/td>\n<td style=\"width: 272.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9978bf64ff03e72a6c40a3b8dad23786_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;&#46;&#50;&#120;&#43;&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 380.406px;\">Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td style=\"width: 272.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01ff35614b9ebfc04893e3ab8e8efc02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#48;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 380.406px;\"><\/td>\n<td style=\"width: 272.406px;\">The <em data-effect=\"italics\">y<\/em>-intercept is (0, 45)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 380.406px;\">Plot the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td style=\"width: 272.406px;\">See graph below.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 380.406px;\">Count out the rise and run to mark the second point. The slope is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01ff35614b9ebfc04893e3ab8e8efc02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#48;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/>; in fraction form this means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26a8b7784b2a69b838272dee0ea243c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"59\" style=\"vertical-align: -12px;\" \/>. Given the scale of our graph, it would be easier to use the equivalent fraction <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6abc2314d1a8a51ca820af056b00acb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#53;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"59\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<td style=\"width: 272.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 380.406px;\">Draw the line.<\/td>\n<td style=\"width: 272.406px;\"><span id=\"eip-id1172184643399\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_013a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596766628\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596766631\" data-type=\"exercise\">\n<div id=\"fs-id1169594011511\" data-type=\"problem\">\n<p id=\"fs-id1169594011514\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7ef966a6fa8d9e37b6ebabe8c817d3be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;&#46;&#53;&#120;&#43;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -4px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596531274\" data-type=\"solution\"><span id=\"fs-id1169596531277\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 70 to 30. The y-axis of the plane runs from negative 20 to 40. The points (0, 25) and (10, 30) are plotted on the line.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_022_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 70 to 30. The y-axis of the plane runs from negative 20 to 40. The points (0, 25) and (10, 30) are plotted on the line.\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596591895\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596591898\" data-type=\"exercise\">\n<div id=\"fs-id1169594049400\" data-type=\"solution\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596591901\" data-type=\"problem\">\n<p id=\"fs-id1169596376698\">Graph the line of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f292aeff437655e26fc3fa8b23d44173_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;&#46;&#49;&#120;&#45;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"105\" style=\"vertical-align: -4px;\" \/> using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169594049400\" data-type=\"solution\"><span id=\"fs-id1169594049403\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 50 to 350. The y-axis of the plane runs from negative 40 to 40. The points (0, negative 30) and (100, negative 20) are plotted on the line.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_023_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 50 to 350. The y-axis of the plane runs from negative 40 to 40. The points (0, negative 30) and (100, negative 20) are plotted on the line.\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596766628\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596766631\" data-type=\"exercise\">\n<div id=\"fs-id1169594011511\" data-type=\"problem\">Now that we have graphed lines by using the slope and <em data-effect=\"italics\">y<\/em>-intercept, let\u2019s summarize all the methods we have used to graph lines. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_05_038\">(Figure)<\/a>.<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596591895\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596591898\" data-type=\"exercise\">\n<div id=\"fs-id1169594049400\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Methods to graph lines<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"CNX_ElemAlg_Figure_04_05_038\" class=\"bc-figure figure\"><span id=\"fs-id1169594103513\" data-type=\"media\" data-alt=\"The table has two rows and four columns. The first row spans all four columns and is a header row. The header is \u201cMethods to Graph Lines\u201d. The second row is made up of four columns. The first column is labeled \u201cPlotting Points\u201d and shows a smaller table with four rows and two columns. The first row is a header row with the first column labeled \u201cx\u201d and the second labeled \u201cy\u201d. The rest of the table is blank. Below the table it reads \u201cFind three points. Plot the points, make sure they line up, then draw the line.\u201d The Second column is labeled \u201cSlope\u2013Intercept\u201d and shows the equation y equals m x, plus b. Below the equation it reads \u201cFind the slope and y-intercept. Start at the y-intercept, then count the slope to get a second point.\u201d The third column is labeled \u201cIntercepts\u201d and shows a smaller table with four rows and two columns. The first row is a header row with the first column labeled \u201cx\u201d and the second labeled \u201cy\u201d. The second row has a 0 in the \u201cx\u201d column and the \u201cy\u201d column is blank. The second row is blank in the \u201cx\u201d column and has a 0 in the \u201cy\u201d column. The third row is blank. Below the table it reads \u201cFind the intercepts and a third point. Plot the points, make sure they line up, then draw the line.\u201d The fourth column is labeled \u201cRecognize Vertical and Horizontal Lines\u201d. Below that it reads \u201cThe equation has only one variable.\u201d The equation x equals a is a vertical line and the equation y equals b is a horizontal line.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_038_img_new.jpg\" alt=\"The table has two rows and four columns. The first row spans all four columns and is a header row. The header is \u201cMethods to Graph Lines\u201d. The second row is made up of four columns. The first column is labeled \u201cPlotting Points\u201d and shows a smaller table with four rows and two columns. The first row is a header row with the first column labeled \u201cx\u201d and the second labeled \u201cy\u201d. The rest of the table is blank. Below the table it reads \u201cFind three points. Plot the points, make sure they line up, then draw the line.\u201d The Second column is labeled \u201cSlope\u2013Intercept\u201d and shows the equation y equals m x, plus b. Below the equation it reads \u201cFind the slope and y-intercept. Start at the y-intercept, then count the slope to get a second point.\u201d The third column is labeled \u201cIntercepts\u201d and shows a smaller table with four rows and two columns. The first row is a header row with the first column labeled \u201cx\u201d and the second labeled \u201cy\u201d. The second row has a 0 in the \u201cx\u201d column and the \u201cy\u201d column is blank. The second row is blank in the \u201cx\u201d column and has a 0 in the \u201cy\u201d column. The third row is blank. Below the table it reads \u201cFind the intercepts and a third point. Plot the points, make sure they line up, then draw the line.\u201d The fourth column is labeled \u201cRecognize Vertical and Horizontal Lines\u201d. Below that it reads \u201cThe equation has only one variable.\u201d The equation x equals a is a vertical line and the equation y equals b is a horizontal line.\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Choose the Most Convenient Method to Graph a Line<\/h1>\n<p id=\"fs-id1169596704824\">Now that we have seen several methods we can use to graph lines, how do we know which method to use for a given equation?<\/p>\n<p id=\"fs-id1169596704828\">While we could plot points, use the slope\u2013intercept form, or find the intercepts for <em data-effect=\"italics\">any<\/em> equation, if we recognize the most convenient way to graph a certain type of equation, our work will be easier. Generally, plotting points is not the most efficient way to graph a line. We saw better methods in sections 4.3, 4.4, and earlier in this section. Let\u2019s look for some patterns to help determine the most convenient method to graph a line.<\/p>\n<p id=\"fs-id1169596377609\">Here are six equations we graphed in this chapter, and the method we used to graph each of them.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cdc1990fc3511f54e9518401ca13c804_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#108;&#108;&#125;&#38;&#32;&#32;&#92;&#116;&#101;&#120;&#116;&#98;&#102;&#123;&#69;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#98;&#102;&#123;&#77;&#101;&#116;&#104;&#111;&#100;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#35;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#120;&#61;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#86;&#101;&#114;&#116;&#105;&#99;&#97;&#108;&#32;&#108;&#105;&#110;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#35;&#32;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#121;&#61;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#111;&#114;&#105;&#122;&#111;&#110;&#116;&#97;&#108;&#32;&#108;&#105;&#110;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#35;&#51;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#120;&#43;&#50;&#121;&#61;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#110;&#116;&#101;&#114;&#99;&#101;&#112;&#116;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#35;&#52;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#32;&#52;&#120;&#45;&#51;&#121;&#61;&#49;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#110;&#116;&#101;&#114;&#99;&#101;&#112;&#116;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#35;&#53;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#121;&#61;&#52;&#120;&#45;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#108;&#111;&#112;&#101;&#45;&#105;&#110;&#116;&#101;&#114;&#99;&#101;&#112;&#116;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#35;&#54;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#121;&#61;&#45;&#120;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#108;&#111;&#112;&#101;&#45;&#105;&#110;&#116;&#101;&#114;&#99;&#101;&#112;&#116;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"148\" width=\"272\" style=\"vertical-align: -70px;\" \/><\/p>\n<p id=\"fs-id1169596399223\">Equations #1 and #2 each have just one variable. Remember, in equations of this form the value of that one variable is constant; it does not depend on the value of the other variable. Equations of this form have graphs that are vertical or horizontal lines.<\/p>\n<p id=\"fs-id1169596319520\">In equations #3 and #4, both <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> are on the same side of the equation. These two equations are of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/>. We substituted <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5e8ef70615fdaee8588017ac1fdd2da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/> to find the <em data-effect=\"italics\">x<\/em>-intercept and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> to find the <em data-effect=\"italics\">y<\/em>-intercept, and then found a third point by choosing another value for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p id=\"fs-id1169594089163\">Equations #5 and #6 are written in slope\u2013intercept form. After identifying the slope and <em data-effect=\"italics\">y<\/em>-intercept from the equation we used them to graph the line.<\/p>\n<p id=\"fs-id1169596453279\">This leads to the following strategy.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Strategy for choosing the most convenient method to graph a line<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169594123488\">Consider the form of the equation.<\/p>\n<ul id=\"fs-id1169594053747\" data-bullet-style=\"bullet\">\n<li>If it only has one variable, it is a vertical or horizontal line.\n<ul id=\"fs-id1169596658475\" data-bullet-style=\"open-circle\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b24e8b3f28f048c85d6ea0f32d59fff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"43\" style=\"vertical-align: 0px;\" \/> is a vertical line passing through the <em data-effect=\"italics\">x<\/em>-axis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bfc522d71f8ae0353ab021fa2a90c360_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/> is a horizontal line passing through the <em data-effect=\"italics\">y<\/em>-axis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<\/ul>\n<\/li>\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> is isolated on one side of the equation, in the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/>, graph by using the slope and y-intercept.\n<ul id=\"fs-id1169596760713\" data-bullet-style=\"open-circle\">\n<li>Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept and then graph.<\/li>\n<\/ul>\n<\/li>\n<li>If the equation is of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/>, find the intercepts.\n<ul id=\"fs-id1169596500601\" data-bullet-style=\"open-circle\">\n<li>Find the <em data-effect=\"italics\">x<\/em>&#8211; and <em data-effect=\"italics\">y<\/em>-intercepts, a third point, and then graph.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596591690\" data-type=\"problem\">\n<p id=\"fs-id1169596591692\">Determine the most convenient method to graph each line.<\/p>\n<p id=\"fs-id1169596395321\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a9ec985c3bc0aa35a95da9940e4def8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/>\u2003b )<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4241bbc12501a58f922b7cc7b6fdc2a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#45;&#51;&#121;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"99\" style=\"vertical-align: -4px;\" \/>\u2003c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49af7f686347e06977fd3a18757933db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: 0px;\" \/>\u2003d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aa4adf762af244c419f3616777f2926c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594051521\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<ol id=\"fs-id1169597615016\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a9ec985c3bc0aa35a95da9940e4def8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/><br \/>\nThis equation has only one variable,<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>. Its graph is a horizontal line crossing the <em data-effect=\"italics\">y<\/em>-axis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4241bbc12501a58f922b7cc7b6fdc2a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#45;&#51;&#121;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"99\" style=\"vertical-align: -4px;\" \/><br \/>\nThis equation is of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/>. The easiest way to graph it will be to find the intercepts and one more point.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49af7f686347e06977fd3a18757933db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: 0px;\" \/><br \/>\nThere is only one variable, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>. The graph is a vertical line crossing the <em data-effect=\"italics\">x<\/em>-axis at 7.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aa4adf762af244c419f3616777f2926c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/><br \/>\nSince this equation is in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/> form, it will be easiest to graph this line by using the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596361008\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596438942\" data-type=\"exercise\">\n<div id=\"fs-id1169596438944\" data-type=\"problem\">\n<p id=\"fs-id1169596438946\">Determine the most convenient method to graph each line: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-64c943eb082c01ef6bb9fde386b62b80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/>\u2003b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0621c4f761e7864714642fcc62d4c42f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/>\u2003c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e8a19f62cbff19c0ff2d9c4eabca6866_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\" \/>\u2003d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-48ebdcda08cf6d53794431f5b209e4f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594053830\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594053833\">a) intercepts\u2003b) horizontal line\u2003c) slope\u2013intercept\u2003d) vertical line<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594051697\" data-type=\"problem\">\n<p id=\"fs-id1169594160383\">Determine the most convenient method to graph each line: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-116dfacb4c2a32bdfb5ab9e852f29986_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>\u2003b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e60b0977d56e0f31cdb904b63a60fda2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"99\" style=\"vertical-align: -12px;\" \/>\u2003c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bdf5fdfeb46a3ca568f85caca31bb50e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/>\u2003d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-968941de010afb17db8ab0fe7d5884bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#51;&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"104\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594112314\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594085183\">a) vertical line\u2003b) slope\u2013intercept\u2003c) horizontal line\u2003d) intercepts<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Graph and Interpret Applications of Slope\u2013Intercept<\/h1>\n<p id=\"fs-id1169596453823\">Many real-world applications are modeled by linear equations. We will take a look at a few applications here so you can see how equations written in slope\u2013intercept form relate to real-world situations.<\/p>\n<p id=\"fs-id1169594028785\">Usually when a linear equation models a real-world situation, different letters are used for the variables, instead of <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em>. The variable names remind us of what quantities are being measured.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596569131\" data-type=\"problem\">\n<p id=\"fs-id1169596569133\">The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0073d36badfd6a1ef0e45782ecc9279b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#53;&#125;&#67;&#43;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"103\" style=\"vertical-align: -12px;\" \/> is used to convert temperatures, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f34f74d98915e33f37a086f8cbfb996a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>, on the Celsius scale to temperatures, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2510519bbe1660dfdffb4195c7287343_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>, on the Fahrenheit scale.<\/p>\n<p id=\"fs-id1169751874566\">a) Find the Fahrenheit temperature for a Celsius temperature of 0.<br \/>\nb) Find the Fahrenheit temperature for a Celsius temperature of 20.<br \/>\nc) Interpret the slope and <em data-effect=\"italics\">F<\/em>-intercept of the equation.<br \/>\nd) Graph the equation.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"fs-id1169596381060\" data-type=\"solution\">\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-765\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<br \/>\nFind the Fahrenheit temperature for a Celsius temperature of 0.<br \/>\nFind <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2510519bbe1660dfdffb4195c7287343_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-273deecff45175c003aa312939a3d01c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/>.<br \/>\nSimplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf7cbc1971ed7b9fe581fbeb0a3a4413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#70;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#53;&#125;&#67;&#43;&#51;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#70;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#53;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#70;&#61;&#51;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"88\" width=\"115\" style=\"vertical-align: -36px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<br \/>\nFind the Fahrenheit temperature for a Celsius temperature of 20.<br \/>\nFind <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2510519bbe1660dfdffb4195c7287343_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0f4f5209e3f1ea4fd9c6430d60005320_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/>.<br \/>\nSimplify.<br \/>\nSimplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-78f16b2a5922956b184e0f8022335a67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#70;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#53;&#125;&#67;&#43;&#51;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#70;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#53;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#70;&#61;&#51;&#54;&#43;&#51;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#70;&#61;&#54;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"110\" width=\"123\" style=\"vertical-align: -47px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596389972\">c) Interpret the slope and <em data-effect=\"italics\">F<\/em>-intercept of the equation.<\/p>\n<p id=\"fs-id1169596653603\">Even though this equation uses <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2510519bbe1660dfdffb4195c7287343_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f34f74d98915e33f37a086f8cbfb996a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>, it is still in slope\u2013intercept form.<\/p>\n<p><span id=\"fs-id1169596515134\" data-type=\"media\" data-alt=\"This image shows three lines of equations. The first line reads y equals m x plus b. The second line reads F equals m C plus b and the third line reads F equals nine fifths times C plus 32.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_024_img_new.jpg\" alt=\"This image shows three lines of equations. The first line reads y equals m x plus b. The second line reads F equals m C plus b and the third line reads F equals nine fifths times C plus 32.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596372283\">The slope, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-509344a5056b415a79243b931e9ef128_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\" \/>, means that the temperature Fahrenheit (<em data-effect=\"italics\">F<\/em>) increases 9 degrees when the temperature Celsius (<em data-effect=\"italics\">C<\/em>) increases 5 degrees.<\/p>\n<p id=\"fs-id1169594008570\">The <em data-effect=\"italics\">F<\/em>-intercept means that when the temperature is 0\u00b0 on the Celsius scale, it is 32\u00b0 on the Fahrenheit scale.<\/p>\n<p id=\"fs-id1169596623952\">d) Graph the equation.<\/p>\n<p id=\"fs-id1169594002104\">We\u2019ll need to use a larger scale than our usual. Start at the <em data-effect=\"italics\">F<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-917d44d6af01c89309f238c39135c1f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#51;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/> then count out the rise of 9 and the run of 5 to get a second point. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_05_039\">(Figure)<\/a>.<\/p>\n<div id=\"CNX_ElemAlg_Figure_04_05_039\" class=\"bc-figure figure\"><span id=\"fs-id1169596400346\" data-type=\"media\" data-alt=\"No Alt Text\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_039_img_new.jpg\" alt=\"No Alt Text\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596531828\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596687493\" data-type=\"exercise\">\n<div id=\"fs-id1169596687495\" data-type=\"problem\">\n<p id=\"fs-id1169596687497\">The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d09358feecf9f199dea6a4947ac86a02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;&#50;&#115;&#43;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: -2px;\" \/> is used to estimate a woman\u2019s height in inches, <em data-effect=\"italics\">h<\/em>, based on her shoe size, <em data-effect=\"italics\">s<\/em>.<\/p>\n<p id=\"fs-id1169751902824\">a) Estimate the height of a child who wears women\u2019s shoe size 0.<br \/>\nb) Estimate the height of a woman with shoe size 8.<br \/>\nc) Interpret the slope and <em data-effect=\"italics\">h<\/em>-intercept of the equation.<br \/>\nd) Graph the equation.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596534829\" data-type=\"solution\">\n<ol id=\"fs-id1169597594096\" class=\"circled\" type=\"a\">\n<li>50 inches<\/li>\n<li>66 inches<\/li>\n<li>The slope, 2, means that the height, <em data-effect=\"italics\">h<\/em>, increases by 2 inches when the shoe size, <em data-effect=\"italics\">s<\/em>, increases by 1. The <em data-effect=\"italics\">h<\/em>-intercept means that when the shoe size is 0, the height is 50 inches.<\/li>\n<li><span id=\"fs-id1169594029134\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable s and runs from negative 2 to 15. The y-axis of the plane represents the variable h and runs from negative 1 to 80. The line begins at the point (0, 50) and goes through the points (8, 66).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_026_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable s and runs from negative 2 to 15. The y-axis of the plane represents the variable h and runs from negative 1 to 80. The line begins at the point (0, 50) and goes through the points (8, 66).\" data-media-type=\"image\/jpeg\" \/><\/span><\/li>\n<\/ol>\n<\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596593374\" data-type=\"problem\">\n<p id=\"fs-id1169596593376\">The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5bacf99abe50fd012f5ec9b0938eb0eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#110;&#43;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"100\" style=\"vertical-align: -12px;\" \/> is used to estimate the temperature in degrees Fahrenheit, <em data-effect=\"italics\">T<\/em>, based on the number of cricket chirps, <em data-effect=\"italics\">n<\/em>, in one minute.<\/p>\n<p id=\"fs-id1169751956325\">a) Estimate the temperature when there are no chirps.<br \/>\nb) Estimate the temperature when the number of chirps in one minute is 100.<br \/>\nc) Interpret the slope and <em data-effect=\"italics\">T<\/em>-intercept of the equation.<br \/>\nd) Graph the equation.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169594137644\" data-type=\"solution\">\n<ol id=\"fs-id1169597818415\" class=\"circled\" type=\"a\">\n<li>40 degrees<\/li>\n<li>65 degrees<\/li>\n<li>The slope, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7fc58100d71714be3c30d3c3b33007fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\" \/>, means that the temperature Fahrenheit (<em data-effect=\"italics\">F<\/em>) increases 1 degree when the number of chirps, <em data-effect=\"italics\">n<\/em>, increases by 4. The <em data-effect=\"italics\">T<\/em>-intercept means that when the number of chirps is 0, the temperature is 40\u00b0.<\/li>\n<li><span id=\"fs-id1169596648790\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable n and runs from 10 to 140 The y-axis of the plane represents the variable T and runs from negative 5 to 75. The line begins at the point (0, 40) and goes through the point (100, 65).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_027_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable n and runs from 10 to 140 The y-axis of the plane represents the variable T and runs from negative 5 to 75. The line begins at the point (0, 40) and goes through the point (100, 65).\" data-media-type=\"image\/jpeg\" \/><\/span><\/li>\n<\/ol>\n<\/div>\n<\/details>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596468179\">The cost of running some types business has two components\u2014a <em data-effect=\"italics\">fixed cost<\/em> and a <em data-effect=\"italics\">variable cost<\/em>. The fixed cost is always the same regardless of how many units are produced. This is the cost of rent, insurance, equipment, advertising, and other items that must be paid regularly. The variable cost depends on the number of units produced. It is for the material and labour needed to produce each item.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596395176\" data-type=\"problem\">\n<p id=\"fs-id1169596395178\">Stella has a home business selling gourmet pizzas. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-96030b226661ca40540bffcfb97bf3c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#52;&#112;&#43;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"94\" style=\"vertical-align: -4px;\" \/> models the relation between her weekly cost, <em data-effect=\"italics\">C<\/em>, in dollars and the number of pizzas, <em data-effect=\"italics\">p<\/em>, that she sells.<\/p>\n<p id=\"fs-id1169754417036\">a) Find Stella\u2019s cost for a week when she sells no pizzas.<br \/>\nb) Find the cost for a week when she sells 15 pizzas.<br \/>\nc) Interpret the slope and <em data-effect=\"italics\">C<\/em>-intercept of the equation.<br \/>\nd) Graph the equation.<\/p>\n<\/div>\n<div id=\"fs-id1169596765745\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172182381935\" class=\"unnumbered unstyled can-break\" summary=\"This figure shows the steps to solve a four part problem. Part (a) is to find Stella\u2019s cost for a week when she sells no pizzas. The equation is C equals 4p plus 25, where C is Stella\u2019s cost and p is the number of pizzas sold. We must find C when p equals 0. Solving for C in the equation C equals 4 times 0 plus 25 yields a value of 25 for C. Stella\u2019s weekly cost is ?25 when she sells no pizzas. Part (b) is to find Stella\u2019s cost for a week when she sells 15 pizzas. Solving for C in the equation C equals 4 times 15 plus 25 yields C equals 60 plus 25 plus 32, which we simplify to C equals 85. Stella\u2019s weekly cost is ?85 when she sells no pizzas. Part (c) is to interpret the slope and C-intercept of the equation. Even though the equation C equals 4p plus 25 uses C and p, it is still in slope-intercept form. The slope, 4, means that the cost increases by ?4 for each pizza Stella sells. The C-intercept means that even when Stella sells no pizzas, her costs for the week are ?25. Part (d) is to graph the equation. We\u2019ll need to use a larger scale than our usual. Start at the C-intercept (0, 25) then count out the rise of 5 and the run of 1 to get a second point. At the very bottom of the figure is a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable p and runs from negative 1 to 20. The y-axis of the plane represents the variable C and runs from negative 1 to 100. The line begins at the point (0, 25) and goes through the point (15, 85).\" data-label=\"\">\n<tbody>\n<tr>\n<td>a) Find Stella&#8217;s cost for a week when she sells no pizzas.<\/td>\n<td><span id=\"eip-id1172185620920\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find <em data-effect=\"italics\">C<\/em> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef3696bb3425b816a345f8115a18fef1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"43\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><span id=\"eip-id1172185620945\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172185620962\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Stella&#8217;s fixed cost is &#36;25 when she sells no pizzas.<\/td>\n<\/tr>\n<tr>\n<td>b) Find the cost for a week when she sells 15 pizzas.<\/td>\n<td><span id=\"eip-id1172182578628\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find <em data-effect=\"italics\">C<\/em> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-71745d8db6496f45e724d38fc0563e87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"51\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><span id=\"eip-id1172182578653\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172180200408\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172180200424\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Stella&#8217;s costs are &#36;85 when she sells 15 pizzas.<\/td>\n<\/tr>\n<tr>\n<td>c) Interpret the slope and <em data-effect=\"italics\">C<\/em>-intercept of the equation.<\/td>\n<td><span id=\"eip-id1172189350891\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>The slope, 4, means that the cost increases by &#36;4 for each pizza Stella sells. The <em data-effect=\"italics\">C<\/em>-intercept means that even when Stella sells no pizzas, her costs for the week are &#36;25.<\/td>\n<\/tr>\n<tr>\n<td>d) Graph the equation. We&#8217;ll need to use a larger scale than our usual. Start at the <em data-effect=\"italics\">C<\/em>-intercept (0, 25) then count out the rise of 4 and the run of 1 to get a second point.<\/td>\n<td><span id=\"eip-id1172189350923\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_028a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596653516\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596653520\" data-type=\"exercise\">\n<div id=\"fs-id1169596653523\" data-type=\"problem\">\n<p id=\"fs-id1169596375236\">Sam drives a delivery van. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e945b872c60d4158e98b2823eb0721f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#48;&#46;&#53;&#109;&#43;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"115\" style=\"vertical-align: -2px;\" \/> models the relation between his weekly cost, <em data-effect=\"italics\">C<\/em>, in dollars and the number of miles, <em data-effect=\"italics\">m<\/em>, that he drives.<\/p>\n<p id=\"fs-id1169751894665\">a) Find Sam\u2019s cost for a week when he drives 0 miles.<br \/>\nb) Find the cost for a week when he drives 250 miles.<br \/>\nc) Interpret the slope and <em data-effect=\"italics\">C<\/em>-intercept of the equation.<br \/>\nd) Graph the equation.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id11695941759711\" data-type=\"solution\">\n<ol id=\"fs-id1169597517137\" class=\"circled\" type=\"a\">\n<li>&#36;60<\/li>\n<li>&#36;185<\/li>\n<li>The slope, 0.5, means that the weekly cost, <em data-effect=\"italics\">C<\/em>, increases by &#36;0.50 when the number of miles driven, <em data-effect=\"italics\">n,<\/em> increases by 1. The <em data-effect=\"italics\">C<\/em>-intercept means that when the number of miles driven is 0, the weekly cost is &#36;60<\/li>\n<li><span id=\"fs-id1169594007893\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 10 to 400. The y-axis of the plane represents the variable C and runs from negative 10 to 300. The line begins at the point (0, 65) and goes through the point (250, 185).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_036_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 10 to 400. The y-axis of the plane represents the variable C and runs from negative 10 to 300. The line begins at the point (0, 65) and goes through the point (250, 185).\" data-media-type=\"image\/jpeg\" \/><\/span><\/li>\n<\/ol>\n<\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596555224\" data-type=\"problem\">\n<p id=\"fs-id1169596555226\">Loreen has a calligraphy business. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-35f07dc02f36b9b20df5994887fe0178_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#49;&#46;&#56;&#110;&#43;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"110\" style=\"vertical-align: -2px;\" \/> models the relation between her weekly cost, <em data-effect=\"italics\">C<\/em>, in dollars and the number of wedding invitations, <em data-effect=\"italics\">n<\/em>, that she writes.<\/p>\n<p id=\"fs-id1169751961255\">a) Find Loreen\u2019s cost for a week when she writes no invitations.<br \/>\nb) Find the cost for a week when she writes 75 invitations.<br \/>\nc) Interpret the slope and <em data-effect=\"italics\">C<\/em>-intercept of the equation.<br \/>\nd) Graph the equation.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169594050309\" data-type=\"solution\">\n<ol id=\"fs-id1169595118573\" class=\"circled\" type=\"a\">\n<li>&#36;35<\/li>\n<li>&#36;170<\/li>\n<li>The slope, 1.8, means that the weekly cost, C, increases by &#36;1.80 when the number of invitations, <em data-effect=\"italics\">n<\/em>, increases by 1.80.<br \/>\nThe <em data-effect=\"italics\">C<\/em>-intercept means that when the number of invitations is 0, the weekly cost is &#36;35.;<\/li>\n<li><span id=\"fs-id1169594028669\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable n and runs from negative 10 to 400. The y-axis of the plane represents the variable C and runs from negative 10 to 300. The line begins at the point (0, 35) and goes through the point (75, 170).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_037_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable n and runs from negative 10 to 400. The y-axis of the plane represents the variable C and runs from negative 10 to 300. The line begins at the point (0, 35) and goes through the point (75, 170).\" data-media-type=\"image\/jpeg\" \/><\/span><\/li>\n<\/ol>\n<\/div>\n<\/details>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Use Slopes to Identify Parallel Lines<\/h1>\n<p id=\"fs-id1169596379736\">The slope of a line indicates how steep the line is and whether it rises or falls as we read it from left to right. Two lines that have the same slope are called parallel lines. Parallel lines never intersect.<\/p>\n<p><span id=\"fs-id1169594029149\" data-type=\"media\" data-alt=\"The figure shows three pairs of lines side-by-side. The pair of lines on the left run diagonally rising from left to right. The pair run side-by-side, not crossing. The pair of lines in the middle run diagonally dropping from left to right. The pair run side-by-side, not crossing. The pair of lines on the right run diagonally also dropping from left to right, but with a lesser slope. The pair run side-by-side, not crossing.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_029_img_new.jpg\" alt=\"The figure shows three pairs of lines side-by-side. The pair of lines on the left run diagonally rising from left to right. The pair run side-by-side, not crossing. The pair of lines in the middle run diagonally dropping from left to right. The pair run side-by-side, not crossing. The pair of lines on the right run diagonally also dropping from left to right, but with a lesser slope. The pair run side-by-side, not crossing.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596394539\">We say this more formally in terms of the rectangular coordinate system. Two lines that have the same slope and different <em data-effect=\"italics\">y<\/em>-intercepts are called parallel lines. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_05_030\">(Figure)<\/a>.<\/p>\n<p>Verify that both lines have the same slope, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-90d4f5754ef62f1058e19fb847c01bf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"50\" style=\"vertical-align: -12px;\" \/>, and different <em data-effect=\"italics\">y<\/em>-intercepts.<\/p>\n<div id=\"CNX_ElemAlg_Figure_04_05_030\" class=\"bc-figure figure\">\n<p><span id=\"fs-id1169596658723\" data-type=\"media\" data-alt=\"The figure shows two lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line goes through the points (negative 5,1) and (5,5). The other line goes through the points (negative 5, negative 4) and (5,0).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_030_img_new.jpg\" alt=\"The figure shows two lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line goes through the points (negative 5,1) and (5,5). The other line goes through the points (negative 5, negative 4) and (5,0).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-id1169594079040\">What about vertical lines? The slope of a vertical line is undefined, so vertical lines don\u2019t fit in the definition above. We say that vertical lines that have different <em data-effect=\"italics\">x<\/em>-intercepts are parallel. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_05_031\">(Figure)<\/a>.<\/p>\n<p>Vertical lines with different <em data-effect=\"italics\">x<\/em>-intercepts are parallel.<\/p>\n<div id=\"CNX_ElemAlg_Figure_04_05_031\" class=\"bc-figure figure\">\n<p><span id=\"fs-id1169596445986\" data-type=\"media\" data-alt=\"The figure shows two vertical lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line goes through the points (2,1) and (2,5). The other line goes through the points (5, negative 4) and (5,0).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_031_img_new.jpg\" alt=\"The figure shows two vertical lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line goes through the points (2,1) and (2,5). The other line goes through the points (5, negative 4) and (5,0).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id1169596767400\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Parallel lines<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596767406\">Parallel lines are lines in the same plane that do not intersect.<\/p>\n<ul id=\"fs-id1169596765521\" data-bullet-style=\"bullet\">\n<li>Parallel lines have the same slope and different <em data-effect=\"italics\">y<\/em>-intercepts.<\/li>\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-334c40e20b6011ce27c41767408d469a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-620bd32ed4ed95ac1b1a29ed0033829f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"23\" style=\"vertical-align: -3px;\" \/> are the slopes of two parallel lines then<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-111242b5510710eea8c2f5ab0c62c314_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#49;&#125;&#61;&#123;&#109;&#125;&#95;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"70\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<li>Parallel vertical lines have different <em data-effect=\"italics\">x<\/em>-intercepts.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169594176048\">Let\u2019s graph the equations <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d1307bebf3c96fca8778786c5d15082d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6a694e2d1d0e8434aa80e88bf78aab5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\" \/> on the same grid. The first equation is already in slope\u2013intercept form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d1307bebf3c96fca8778786c5d15082d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\" \/>. We solve the second equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-325a2f1cd8f9f0dd41d6743911102570_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#120;&#43;&#121;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#121;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#50;&#120;&#45;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"159\" style=\"vertical-align: -15px;\" \/><\/p>\n<p id=\"fs-id1169596437484\">Graph the lines.<\/p>\n<p><span id=\"fs-id1169596437487\" data-type=\"media\" data-alt=\"The figure shows two lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line goes through the points (negative 4, 7) and (3, negative 7). The other line goes through the points (negative 2, 7) and (5, negative 7).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_032_img_new.jpg\" alt=\"The figure shows two lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line goes through the points (negative 4, 7) and (3, negative 7). The other line goes through the points (negative 2, 7) and (5, negative 7).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169594123582\">Notice the lines look parallel. What is the slope of each line? What is the <em data-effect=\"italics\">y<\/em>-intercept of each line?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b4b5e673fba1d3c3b88420345595d8d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#108;&#99;&#99;&#108;&#125;&#121;&#38;&#61;&#38;&#32;&#109;&#120;&#43;&#98;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#38;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#32;&#121;&#38;&#32;&#61;&#38;&#32;&#109;&#120;&#43;&#98;&#32;&#92;&#92;&#32;&#121;&#32;&#38;&#32;&#61;&#32;&#38;&#32;&#45;&#50;&#120;&#43;&#51;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#38;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#121;&#38;&#61;&#32;&#38;&#32;&#45;&#50;&#120;&#45;&#49;&#32;&#92;&#92;&#32;&#32;&#109;&#38;&#32;&#61;&#32;&#38;&#32;&#45;&#50;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#38;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#109;&#38;&#32;&#61;&#32;&#38;&#32;&#45;&#50;&#32;&#92;&#92;&#32;&#98;&#38;&#32;&#61;&#32;&#38;&#32;&#51;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#40;&#48;&#44;&#32;&#51;&#41;&#125;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#38;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#98;&#32;&#38;&#32;&#61;&#32;&#38;&#32;&#45;&#49;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#40;&#48;&#44;&#32;&#45;&#49;&#41;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"83\" width=\"352\" style=\"vertical-align: -38px;\" \/><\/p>\n<p id=\"fs-id1169596296181\">The slopes of the lines are the same and the <em data-effect=\"italics\">y<\/em>-intercept of each line is different. So we know these lines are parallel.<\/p>\n<p id=\"fs-id1169594083617\">Since parallel lines have the same slope and different <em data-effect=\"italics\">y<\/em>-intercepts, we can now just look at the slope\u2013intercept form of the equations of lines and decide if the lines are parallel.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594083633\" data-type=\"problem\">\n<p id=\"fs-id1169594160247\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4fa0b37b12e2ed9b6d126e5523cd6dbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bf63dd4da6841d861b09af625fdb5c74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/> are parallel.<\/p>\n<\/div>\n<div id=\"fs-id1169596244418\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-562\" summary=\"\/\">\n<tbody>\n<tr>\n<td>Solve the first equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7ac3737fa715857eeddcc07898362bde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#99;&#108;&#125;&#32;&#51;&#120;&#45;&#50;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#54;&#32;&#92;&#92;&#32;&#32;&#45;&#50;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#45;&#51;&#120;&#43;&#54;&#32;&#92;&#92;&#32;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#50;&#121;&#125;&#123;&#45;&#50;&#125;&#38;&#32;&#61;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#51;&#120;&#43;&#54;&#125;&#123;&#45;&#50;&#125;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"77\" width=\"171\" style=\"vertical-align: -35px;\" \/><\/td>\n<td>and<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bf63dd4da6841d861b09af625fdb5c74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>The equation is now in slope-intercept form.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4f14aa1b510f564bfd6001edb00ce08d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\" \/><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The equation of the second line is already in slope-intercept form.<\/td>\n<td><\/td>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bf63dd4da6841d861b09af625fdb5c74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Identify the slope and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept of both lines.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d99bb37ad9861aa3b42a963e3245cb16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#125;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#120;&#45;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#32;&#121;&#61;&#109;&#120;&#43;&#98;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"94\" width=\"88\" style=\"vertical-align: -75px;\" \/><\/td>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-12929bb297724ca46a332d469766f326_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#125;&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#120;&#43;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#121;&#61;&#109;&#120;&#43;&#98;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"94\" width=\"88\" style=\"vertical-align: -42px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>y-intercept is (0, \u22123)<\/td>\n<td><\/td>\n<td>y-intercept is (0, 1)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594178196\">The lines have the same slope and different <em data-effect=\"italics\">y<\/em>-intercepts and so they are parallel. You may want to graph the lines to confirm whether they are parallel.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594178209\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594178213\" data-type=\"exercise\">\n<div id=\"fs-id1169594178215\" data-type=\"problem\">\n<p id=\"fs-id1169594178217\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8107fee33ef60da2723968b6f7eab4e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#53;&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a9505815b0ddf03c2b223fe085661683_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"100\" style=\"vertical-align: -12px;\" \/> are parallel.<\/p>\n<\/div>\n<div id=\"fs-id1169596535500\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596535502\">parallel<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596535514\" data-type=\"problem\">\n<p id=\"fs-id1169596535516\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b37c0dcff66f7a836d76a4680e3137c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ab9ea172a7f4a642b66a52f26af6d288_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/> are parallel.<\/p>\n<\/div>\n<div id=\"fs-id1169596446494\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596446496\">parallel<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596535508\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596535512\" data-type=\"exercise\">\n<div id=\"fs-id1169596446494\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596685319\" data-type=\"problem\">\n<p id=\"fs-id1169596685321\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-53923be0c534e9cf06b453317eed3f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8e36d35d8563f5053efd9935e88634f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/> are parallel.<\/p>\n<\/div>\n<div id=\"fs-id1169596445675\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-410\" summary=\"\/\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bdaa8b33642debd802cebda3ac265230_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#121;&#61;&#45;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#121;&#61;&#48;&#120;&#45;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"83\" style=\"vertical-align: -15px;\" \/><\/td>\n<td>and<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4dfe542286987c028f4c3334f17c20f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#121;&#61;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#121;&#61;&#48;&#120;&#43;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"83\" style=\"vertical-align: -15px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write each equation in slope-intercept form.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b9d30f9bfb52517eea294eb673947394_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6f3ff8e9cb8e2b6af260c35876919d8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Since there is no <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> term we write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02997385b3462bb457fc7c0177d5abac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Identify the slope and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept of both lines.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-677ddb33cbc84708fb03582c5c4e82bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-677ddb33cbc84708fb03582c5c4e82bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>y-intercept is (0, 4)<\/td>\n<td><\/td>\n<td>y-intercept is (0, 3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594137437\">The lines have the same slope and different <em data-effect=\"italics\">y<\/em>-intercepts and so they are parallel.<\/p>\n<p id=\"fs-id1169594137460\">There is another way you can look at this example. If you recognize right away from the equations that these are horizontal lines, you know their slopes are both 0. Since the horizontal lines cross the <em data-effect=\"italics\">y<\/em>-axis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-53923be0c534e9cf06b453317eed3f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/> and at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8e36d35d8563f5053efd9935e88634f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/>, we know the <em data-effect=\"italics\">y<\/em>-intercepts are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-42f3c0bd5adc0ec0fa1707d7989e5c00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef24d382319a3ce81f280194edba003a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>. The lines have the same slope and different <em data-effect=\"italics\">y<\/em>-intercepts and so they are parallel.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596446494\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596446319\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596446324\" data-type=\"exercise\">\n<div id=\"fs-id1169596446326\" data-type=\"problem\">\n<p id=\"fs-id1169596365608\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-48a5d37560b8f593c417bc913eae1b98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a9ec985c3bc0aa35a95da9940e4def8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/> are parallel.<\/p>\n<\/div>\n<div id=\"fs-id1169596365636\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596457923\">parallel<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596457936\" data-type=\"problem\">\n<p id=\"fs-id1169596457938\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0e3ca3f6eb8810e090b4ceee7f6e129b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ee7bf59b42611ad4534a6d8ca47648e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"55\" style=\"vertical-align: -4px;\" \/> are parallel.<\/p>\n<\/div>\n<div id=\"fs-id1169596371937\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596371939\">parallel<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596457930\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596457934\" data-type=\"exercise\">\n<div id=\"fs-id1169596371937\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169595152111\" data-type=\"problem\">\n<p id=\"fs-id1169596371952\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3e213d8d687e32831c24e16c432b60e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/> are parallel.<\/p>\n<\/div>\n<div id=\"fs-id1169594188927\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<div id=\"fs-id1169596634997\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3e213d8d687e32831c24e16c432b60e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/div>\n<p id=\"fs-id1169596635017\">Since there is no<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>, the equations cannot be put in slope\u2013intercept form. But we recognize them as equations of vertical lines. Their <em data-effect=\"italics\">x<\/em>-intercepts are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/>. Since their <em data-effect=\"italics\">x<\/em>-intercepts are different, the vertical lines are parallel.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594060048\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594060052\" data-type=\"exercise\">\n<div id=\"fs-id1169594030452\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594060048\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594060052\" data-type=\"exercise\">\n<div id=\"fs-id1169594030452\" data-type=\"problem\">\n<p id=\"fs-id1169594030454\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3330a01aa4d7d81947b71297d8623d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3e213d8d687e32831c24e16c432b60e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/> are parallel.<\/p>\n<\/div>\n<div id=\"fs-id1169594087033\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594087035\">parallel<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594087048\" data-type=\"problem\">\n<p id=\"fs-id1169594087050\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1dc438da70f358c2eb1bf64a8b7ea4b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-77758982e3a224cd6ee6269fafa47055_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/> are parallel.<\/p>\n<\/div>\n<div id=\"fs-id1169594158056\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594158058\">parallel<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594087042\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594087046\" data-type=\"exercise\">\n<div id=\"fs-id1169594158056\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594158069\" data-type=\"problem\">\n<p id=\"fs-id1169594158071\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e09b4ae6d312635fcb8ec259a322e66d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8a1d3fcae116f81797ba2e220b8a1250_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#120;&#43;&#51;&#121;&#61;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"118\" style=\"vertical-align: -4px;\" \/> are parallel. You may want to graph these lines, too, to see what they look like.<\/p>\n<\/div>\n<div id=\"fs-id1169596438801\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-771\" style=\"width: 789px; height: 255px;\" summary=\".\">\n<tbody>\n<tr>\n<td style=\"width: 165.406px;\"><\/td>\n<td style=\"width: 197.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e09b4ae6d312635fcb8ec259a322e66d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 34.4062px;\">and<\/td>\n<td style=\"width: 332.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8a1d3fcae116f81797ba2e220b8a1250_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#120;&#43;&#51;&#121;&#61;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"118\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 165.406px;\">The first equation is already in slope-intercept form.<\/td>\n<td style=\"width: 197.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e09b4ae6d312635fcb8ec259a322e66d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 34.4062px;\"><\/td>\n<td style=\"width: 332.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 165.406px;\">Solve the second equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td style=\"width: 197.406px;\"><\/td>\n<td style=\"width: 34.4062px;\"><\/td>\n<td style=\"width: 332.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-83d1299eca648fbee2a5562499d7159c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#32;&#45;&#54;&#120;&#43;&#51;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#45;&#57;&#32;&#92;&#92;&#32;&#32;&#51;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#54;&#120;&#45;&#57;&#32;&#92;&#92;&#32;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#121;&#125;&#123;&#51;&#125;&#38;&#32;&#61;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#54;&#120;&#45;&#57;&#125;&#123;&#51;&#125;&#32;&#92;&#92;&#32;&#32;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#50;&#120;&#45;&#51;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"96\" width=\"170\" style=\"vertical-align: -44px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 165.406px;\">The second equation is now in slope-intercept form.<\/td>\n<td style=\"width: 197.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e09b4ae6d312635fcb8ec259a322e66d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 34.4062px;\"><\/td>\n<td style=\"width: 332.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 165.406px;\">Identify the slope and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept of both lines.<\/td>\n<td style=\"width: 197.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-223d455f4966fcfe6ea090fadb1c02f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#125;&#32;&#121;&#32;&#61;&#50;&#120;&#45;&#51;&#32;&#92;&#92;&#32;&#32;&#121;&#61;&#109;&#120;&#43;&#98;&#92;&#92;&#32;&#32;&#109;&#32;&#61;&#50;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"88\" style=\"vertical-align: -22px;\" \/><\/td>\n<td style=\"width: 34.4062px;\"><\/td>\n<td style=\"width: 332.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c45fab20420885b161510eff56053326_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#125;&#32;&#121;&#61;&#50;&#120;&#45;&#51;&#32;&#92;&#92;&#32;&#32;&#121;&#61;&#109;&#120;&#43;&#98;&#32;&#92;&#92;&#32;&#32;&#109;&#61;&#50;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"88\" style=\"vertical-align: -22px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 165.406px;\"><\/td>\n<td style=\"width: 197.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e373dd0300831fc831e82fcee5cb16c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#105;&#110;&#116;&#101;&#114;&#99;&#101;&#112;&#116;&#32;&#105;&#115;&#32;&#40;&#48;&#44;&#32;&#45;&#51;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"155\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 34.4062px;\"><\/td>\n<td style=\"width: 332.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e373dd0300831fc831e82fcee5cb16c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#105;&#110;&#116;&#101;&#114;&#99;&#101;&#112;&#116;&#32;&#105;&#115;&#32;&#40;&#48;&#44;&#32;&#45;&#51;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"155\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596445891\">The lines have the same slope, but they also have the same <em data-effect=\"italics\">y<\/em>-intercepts. Their equations represent the same line. They are not parallel; they are the same line.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596445904\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596445908\" data-type=\"exercise\">\n<div id=\"fs-id1169596445910\" data-type=\"problem\">\n<p id=\"fs-id1169596445912\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1d5fb4f1ddaf39fbf01ba9de35a4a018_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"99\" style=\"vertical-align: -12px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23d557961f719ff07c20022869f0746c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#50;&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/> are parallel.<\/p>\n<\/div>\n<div id=\"fs-id1169596445997\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596445999\">not parallel; same line<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596446012\" data-type=\"problem\">\n<p id=\"fs-id1169596446014\">Use slopes and <em data-effect=\"italics\">y<\/em>-intercepts to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24c5cedc6f11b3724fdb0b7203a77ae1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0ff93eb9bb91e4a9bd6b32f826b8acd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#52;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/> are parallel.<\/p>\n<\/div>\n<div id=\"fs-id1169596215980\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596215982\">not parallel; same line<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Use Slopes to Identify Perpendicular Lines<\/h1>\n<p id=\"fs-id1169596754462\">Let\u2019s look at the lines whose equations are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-20ee4f8c89ede96eba0b4f8213f36454_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5f92dc0615b9e8759e302e79781dc54f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/>, shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_05_033\">(Figure)<\/a>.<\/p>\n<div id=\"CNX_ElemAlg_Figure_04_05_033\" class=\"bc-figure figure\"><span id=\"fs-id1169596648808\" data-type=\"media\" data-alt=\"The figure shows two lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line is labeled with the equation y equals negative 4x plus 2 and goes through the points (0,2) and (1, negative 2). The other line is labeled with the equation y equals one fourth x minus 1 and goes through the points (0, negative 1) and (4,0).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_033_img_new.jpg\" alt=\"The figure shows two lines graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. One line is labeled with the equation y equals negative 4x plus 2 and goes through the points (0,2) and (1, negative 2). The other line is labeled with the equation y equals one fourth x minus 1 and goes through the points (0, negative 1) and (4,0).\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<p id=\"fs-id1169596648827\">These lines lie in the same plane and intersect in right angles. We call these lines perpendicular.<\/p>\n<p id=\"fs-id1169594178156\">What do you notice about the slopes of these two lines? As we read from left to right, the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-20ee4f8c89ede96eba0b4f8213f36454_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/> rises, so its slope is positive. The line<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5f92dc0615b9e8759e302e79781dc54f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/> drops from left to right, so it has a negative slope. Does it make sense to you that the slopes of two perpendicular lines will have opposite signs?<\/p>\n<p id=\"fs-id1169596754391\">If we look at the slope of the first line, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-29ef3b296fc11614ba5722ecd93b9333_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#49;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"58\" style=\"vertical-align: -12px;\" \/>, and the slope of the second line, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-03cf600087b39cbe78008f54f91b7800_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#50;&#125;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"70\" style=\"vertical-align: -3px;\" \/>, we can see that they are <em data-effect=\"italics\">negative reciprocals<\/em> of each other. If we multiply them, their product is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5f271135c55d98d18c90dad56dd36328_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#123;&#109;&#125;&#95;&#123;&#49;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#109;&#125;&#95;&#123;&#50;&#125;&#32;&#92;&#92;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#45;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"66\" width=\"59\" style=\"vertical-align: -29px;\" \/><\/p>\n<p id=\"fs-id1169594243066\">This is always true for <span class=\"no-emphasis\" data-type=\"term\">perpendicular lines<\/span> and leads us to this definition.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Perpendicular lines<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169594243075\"><strong data-effect=\"bold\">Perpendicular lines<\/strong> are lines in the same plane that form a right angle.<\/p>\n<p id=\"fs-id1169594243080\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-334c40e20b6011ce27c41767408d469a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-620bd32ed4ed95ac1b1a29ed0033829f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"23\" style=\"vertical-align: -3px;\" \/> are the slopes of two perpendicular lines, then:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2a82c65557d19ba2b26b665075f9de08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#49;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#109;&#125;&#95;&#123;&#50;&#125;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"105\" style=\"vertical-align: -3px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-33d42765281895895a394e5fec26e42d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#49;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#49;&#125;&#123;&#123;&#109;&#125;&#95;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"73\" style=\"vertical-align: -15px;\" \/><\/p>\n<p id=\"fs-id1169596598032\">Vertical lines and horizontal lines are always perpendicular to each other.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596598036\">We were able to look at the slope\u2013intercept form of linear equations and determine whether or not the lines were parallel. We can do the same thing for perpendicular lines.<\/p>\n<p id=\"fs-id1169596598043\">We find the slope\u2013intercept form of the equation, and then see if the slopes are negative reciprocals. If the product of the slopes is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>, the lines are perpendicular. Perpendicular lines may have the same <em data-effect=\"italics\">y<\/em>-intercepts.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596557450\" data-type=\"problem\">\n<p id=\"fs-id1169596557452\">Use slopes to determine if the lines, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-af38bb4fe99c6c73393002581fd81410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#53;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"96\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1bd2b2790c6abdf31b04c3a01664986c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#53;&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/> are perpendicular.<\/p>\n<\/div>\n<div id=\"fs-id1169596360728\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-528\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>The first equation is already in slope-intercept form.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7c465293f2855b9a53cc825d0537c1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#32;&#61;&#32;&#45;&#53;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Solve the second equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1c824a8110d121867c10a6a2b5aab599_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#99;&#108;&#125;&#32;&#120;&#45;&#53;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#53;&#32;&#92;&#92;&#32;&#32;&#45;&#53;&#121;&#38;&#32;&#61;&#32;&#38;&#45;&#120;&#43;&#53;&#32;&#92;&#92;&#32;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#53;&#121;&#125;&#123;&#45;&#53;&#125;&#38;&#32;&#61;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#120;&#43;&#53;&#125;&#123;&#45;&#53;&#125;&#32;&#92;&#92;&#32;&#32;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#120;&#45;&#49;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"114\" width=\"153\" style=\"vertical-align: -54px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Identify the slope of each line.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5db6484d967426898befce9554b9b60d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#99;&#108;&#125;&#32;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#45;&#53;&#120;&#45;&#52;&#32;&#92;&#92;&#32;&#32;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#109;&#120;&#43;&#98;&#32;&#92;&#92;&#32;&#32;&#123;&#109;&#125;&#95;&#123;&#49;&#125;&#38;&#32;&#61;&#32;&#38;&#32;&#45;&#53;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"133\" style=\"vertical-align: -25px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-398040727937887a9a4b1c8d39d052ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#99;&#108;&#125;&#32;&#121;&#38;&#32;&#61;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#120;&#45;&#49;&#32;&#92;&#92;&#32;&#32;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#109;&#120;&#43;&#98;&#32;&#92;&#92;&#32;&#32;&#123;&#109;&#125;&#95;&#123;&#50;&#125;&#38;&#32;&#61;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"94\" width=\"125\" style=\"vertical-align: -42px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594239596\">The slopes are negative reciprocals of each other, so the lines are perpendicular. We check by multiplying the slopes,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5e3696491c3663ae3c1fcccbde5c6801_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#123;&#109;&#125;&#95;&#123;&#49;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#109;&#125;&#95;&#123;&#50;&#125;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#45;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#45;&#49;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"95\" width=\"61\" style=\"vertical-align: -44px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596498259\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596379746\" data-type=\"exercise\">\n<div id=\"fs-id1169596379748\" data-type=\"problem\">\n<p id=\"fs-id1169596379750\">Use slopes to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4fc90afade1fa88a952541d19de3fa12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-44d51366d0dd5b52e51e26d170e01d23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#51;&#121;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/> are perpendicular.<\/p>\n<\/div>\n<div id=\"fs-id1169596379786\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596379788\">perpendicular<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596636409\" data-type=\"problem\">\n<p id=\"fs-id1169596636411\">Use slopes to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-36dc4f0038d296bd0274fc26ff822a87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-94a451fcd15dc0f99be1aad8c81d1253_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#50;&#121;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"97\" style=\"vertical-align: -4px;\" \/> are perpendicular.<\/p>\n<\/div>\n<div id=\"fs-id1169594138057\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594138060\">perpendicular<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596636403\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596636407\" data-type=\"exercise\">\n<div id=\"fs-id1169594138057\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 17<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594138070\" data-type=\"problem\">\n<p id=\"fs-id1169594138072\">Use slopes to determine if the lines, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-806630d1fc85c585b6fa802250798834_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#43;&#50;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6c4b0bde914ca9d55c5b9541c686b37d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#55;&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/> are perpendicular.<\/p>\n<\/div>\n<div id=\"fs-id1169596453923\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-682\" summary=\".\">\n<tbody>\n<tr>\n<td>Solve the equations for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c2749c9f5a0ca9253f1d8b42805e73c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#99;&#108;&#125;&#55;&#120;&#43;&#50;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#51;&#32;&#32;&#92;&#92;&#32;&#50;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#45;&#55;&#120;&#43;&#51;&#32;&#92;&#92;&#32;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#121;&#125;&#123;&#50;&#125;&#38;&#32;&#61;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#55;&#120;&#43;&#51;&#125;&#123;&#50;&#125;&#32;&#92;&#92;&#32;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#50;&#125;&#120;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"174\" style=\"vertical-align: -53px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-758fe8d2a4cbae3547dc7ff6b4866bed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#99;&#108;&#125;&#32;&#50;&#120;&#43;&#55;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#53;&#32;&#92;&#92;&#32;&#32;&#55;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#45;&#50;&#120;&#43;&#53;&#32;&#92;&#92;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#121;&#125;&#123;&#55;&#125;&#38;&#32;&#61;&#32;&#38;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#50;&#120;&#43;&#53;&#125;&#123;&#55;&#125;&#32;&#92;&#92;&#32;&#32;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#55;&#125;&#120;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#55;&#125;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"174\" style=\"vertical-align: -53px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Identify the slope of each line.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-83b0b02bf5162c02f2c968ad6dac1624_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#99;&#108;&#125;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#109;&#120;&#43;&#98;&#32;&#92;&#92;&#32;&#123;&#109;&#125;&#95;&#123;&#49;&#125;&#38;&#32;&#61;&#32;&#38;&#32;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#50;&#125;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"125\" style=\"vertical-align: -24px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-364da3abc752feede57b28ab02818609_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#99;&#108;&#125;&#32;&#121;&#38;&#32;&#61;&#32;&#38;&#32;&#109;&#120;&#43;&#98;&#32;&#92;&#92;&#32;&#123;&#109;&#125;&#95;&#123;&#50;&#125;&#38;&#32;&#61;&#32;&#38;&#32;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#55;&#125;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"125\" style=\"vertical-align: -24px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"eip-901\">The slopes are reciprocals of each other, but they have the same sign. Since they are not negative reciprocals, the lines are not perpendicular.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596446075\" data-type=\"exercise\">\n<div id=\"fs-id1169596446077\" data-type=\"problem\">\n<p id=\"fs-id1169596446079\">Use slopes to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-616115ed4f97040ba3f616f3affcf347_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#43;&#52;&#121;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b0d38f4883c535dd9c9e0f00241968e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#53;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/> are perpendicular.<\/p>\n<\/div>\n<div id=\"fs-id1169596446120\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596446122\">not perpendicular<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596548041\" data-type=\"problem\">\n<p id=\"fs-id1169596548043\">Use slopes to determine if the lines <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-12834e4eb56683b7b17fdff40512535d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#57;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-18e6f6ce7f34893d7fab02424fb1bf94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;&#45;&#50;&#121;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\" \/> are perpendicular.<\/p>\n<\/div>\n<div id=\"fs-id1169594236075\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594236077\">not perpendicular<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594236084\" class=\"media-2\" data-type=\"note\">\n<p id=\"fs-id1169594236088\">Access this online resource for additional instruction and practice with graphs.<\/p>\n<ul id=\"fs-id1169594236091\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/25GraphPractice\">Explore the Relation Between a Graph and the Slope\u2013Intercept Form of an Equation of a Line<\/a><\/li>\n<\/ul>\n<\/div>\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"fs-id1169594137963\" data-bullet-style=\"bullet\">\n<li><strong>The slope\u2013intercept form of an equation of a line with slope<\/strong> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-05dbabd42fe84ba97e673be0628c5974_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"37\" style=\"vertical-align: -4px;\" \/> is, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<li><strong data-effect=\"bold\">Graph a Line Using its Slope and <em data-effect=\"italics\">y<\/em>-Intercept<\/strong>\n<ol id=\"fs-id1169596457899\" class=\"stepwise\" type=\"1\">\n<li>Find the slope-intercept form of the equation of the line.<\/li>\n<li>Identify the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/li>\n<li>Plot the <em data-effect=\"italics\">y<\/em>-intercept.<\/li>\n<li>Use the slope formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7bf3b27f8bf32d800686f5f7ddef6962_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#105;&#115;&#101;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#117;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"68\" style=\"vertical-align: -12px;\" \/> to identify the rise and the run.<\/li>\n<li>Starting at the <em data-effect=\"italics\">y<\/em>-intercept, count out the rise and run to mark the second point.<\/li>\n<li>Connect the points with a line.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Strategy for Choosing the Most Convenient Method to Graph a Line:<\/strong> Consider the form of the equation.\n<ul id=\"fs-id1169596654511\" data-bullet-style=\"open-circle\">\n<li>If it only has one variable, it is a vertical or horizontal line.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b24e8b3f28f048c85d6ea0f32d59fff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"43\" style=\"vertical-align: 0px;\" \/> is a vertical line passing through the <em data-effect=\"italics\">x<\/em>-axis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bfc522d71f8ae0353ab021fa2a90c360_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/> is a horizontal line passing through the <em data-effect=\"italics\">y<\/em>-axis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> is isolated on one side of the equation, in the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/>, graph by using the slope and <em data-effect=\"italics\">y<\/em>-intercept.<br \/>\nIdentify the slope and <em data-effect=\"italics\">y<\/em>-intercept and then graph.<\/li>\n<li>If the equation is of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/>, find the intercepts.<br \/>\nFind the <em data-effect=\"italics\">x<\/em>&#8211; and <em data-effect=\"italics\">y<\/em>-intercepts, a third point, and then graph.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Parallel lines are lines in the same plane that do not intersect.<\/strong>\n<ul id=\"fs-id1169594137035\" data-bullet-style=\"open-circle\">\n<li>Parallel lines have the same slope and different <em data-effect=\"italics\">y<\/em>-intercepts.<\/li>\n<li>If <em data-effect=\"italics\">m<\/em><sub>1<\/sub> and <em data-effect=\"italics\">m<\/em><sub>2<\/sub> are the slopes of two parallel lines then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-111242b5510710eea8c2f5ab0c62c314_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#49;&#125;&#61;&#123;&#109;&#125;&#95;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"70\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<li>Parallel vertical lines have different <em data-effect=\"italics\">x<\/em>-intercepts.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Perpendicular lines are lines in the same plane that form a right angle.<\/strong>\n<ul id=\"fs-id1169594154465\" data-bullet-style=\"open-circle\">\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1379f3a2be0ed9054b14044f57d2bea9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#49;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#109;&#125;&#95;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/> are the slopes of two perpendicular lines, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2a82c65557d19ba2b26b665075f9de08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#49;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#109;&#125;&#95;&#123;&#50;&#125;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"105\" style=\"vertical-align: -3px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-33d42765281895895a394e5fec26e42d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#49;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#49;&#125;&#123;&#123;&#109;&#125;&#95;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"73\" style=\"vertical-align: -15px;\" \/>.<\/li>\n<li>Vertical lines and horizontal lines are always perpendicular to each other.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h1 data-type=\"title\">Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1169594168892\">\n<dt>parallel lines<\/dt>\n<dd id=\"fs-id1169594168896\">Lines in the same plane that do not intersect.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594168900\">\n<dt>perpendicular lines<\/dt>\n<dd id=\"fs-id1169594168905\">Lines in the same plane that form a right angle.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594168910\">\n<dt>slope-intercept form of an equation of a line<\/dt>\n<dd id=\"fs-id1169594168914\">The slope\u2013intercept form of an equation of a line with slope <img loading=\"lazy\" decoding=\"async\" class=\"ql-img-inline-formula quicklatex-auto-format\" title=\"Rendered by QuickLaTeX.com\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c87c998129133199e3b4192e87f227b5_l3.svg#fixme#fixme\" alt=\"m\" width=\"15\" height=\"8\" \/> and <em data-effect=\"italics\">y<\/em>-intercept, <img loading=\"lazy\" decoding=\"async\" class=\"ql-img-inline-formula quicklatex-auto-format\" title=\"Rendered by QuickLaTeX.com\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-7e0694338984ab8cffa0b091f76597ea_l3.svg#fixme#fixme\" alt=\"\\left(0,b\\right)\" width=\"37\" height=\"18\" \/> is, <img loading=\"lazy\" decoding=\"async\" class=\"ql-img-inline-formula quicklatex-auto-format\" title=\"Rendered by QuickLaTeX.com\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-7a6e90cb6018a244ec5be6b51fc02aef_l3.svg#fixme#fixme\" alt=\"y=mx+b\" width=\"88\" height=\"17\" \/>.<\/dd>\n<\/dl>\n<\/div>\n<h1 data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1169594078639\">Recognize the Relation Between the Graph and the Slope\u2013Intercept Form of an Equation of a Line<\/h2>\n<p id=\"fs-id1169594078646\">In the following exercises, use the graph to find the slope and y-intercept of each line. Compare the values to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 1293px;\">\n<tbody>\n<tr style=\"height: 398px;\">\n<td style=\"width: 49.9086%; height: 398px;\"><span id=\"fs-id1169596445768\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1,2).\">1.<\/span><\/p>\n<p><span id=\"fs-id1169596445768\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1,2).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_202_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1,2).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596445781\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d76269f8d9b324873c9b8e3993ef6892_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/td>\n<td style=\"width: 50.0914%; height: 398px;\"><span id=\"fs-id1169594078670\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 5) and (1, negative 2).\">2.<\/span><\/p>\n<p><span id=\"fs-id1169594078670\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 5) and (1, negative 2).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_201_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 5) and (1, negative 2).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169594262852\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-47bdbf719e41e4cd61a7a609f53c9186_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 398px;\">\n<td style=\"width: 49.9086%; height: 398px;\"><span id=\"fs-id1169596649110\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (1, negative 2).\">3.<\/span><\/p>\n<p><span id=\"fs-id1169596649110\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (1, negative 2).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_204_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (1, negative 2).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596445922\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9464e80989a4433405a822135673f492_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/td>\n<td style=\"width: 50.0914%; height: 398px;\"><span id=\"fs-id1169594008239\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,4) and (1,3).\">4.<\/span><\/p>\n<p><span id=\"fs-id1169594008239\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,4) and (1,3).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_203_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,4) and (1,3).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169594008252\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a47a249be356e3261dd0f2ebe6f9d2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 481px;\">\n<td style=\"width: 49.9086%; height: 481px;\"><span id=\"fs-id1169596541210\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,3) and (1,5).\">5.<\/span><\/p>\n<p><span id=\"fs-id1169596541210\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,3) and (1,5).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_206_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,3) and (1,5).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596541223\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22d37bcaaf5f1c35ded6304400d85412_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"100\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/td>\n<td style=\"width: 50.0914%; height: 481px;\"><span id=\"fs-id1169594137785\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 3).\">6.<\/span><\/p>\n<p><span id=\"fs-id1169594137785\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 3).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_205_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 3).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169594137798\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2e1ed76d5373469bd2126fe9167b65aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"99\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596639992\">Identify the Slope and y-Intercept From an Equation of a Line<\/h2>\n<p id=\"fs-id1169596639999\">In the following exercises, identify the slope and y-intercept of each line.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 49.9086%;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d86990fb4c0c422e7d1fe864d6be456d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#57;&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aeb7d300b5e6a39579b96381b452b464_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#55;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-263630aa651498483a067b5c26be24b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">10.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-365dbe543084f57b9dcf20ae2e3db1d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#54;&#120;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27ba90acf701f3c2ff6838eb7b4ef0d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f5e5d8d536bd15610418e85b413562ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-08400042b239acbc3c9079d079a5ca2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#43;&#51;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9ea47da93050a9bc225755aa6d085ac7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#43;&#52;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1cae67a7199d636eafb4c5908863321e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#45;&#51;&#121;&#61;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a43cca06f003211fad0af917475c837b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#45;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169594240518\">Graph a Line Using Its Slope and Intercept<\/h2>\n<p id=\"fs-id1169594240524\">In the following exercises, graph the line of each equation using its slope and y-intercept.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\">\n<tbody>\n<tr>\n<td style=\"width: 49.9086%;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9bf5d7a264c371a4ffdc73e723eb682f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bf87a2c643220e6f9ee4d0f1c0e0e37d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e09b4ae6d312635fcb8ec259a322e66d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-09acfc77aa1f355947c21a5c0e345588_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a0b0632b79ec7647ad0d6e83721c5ad2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f511f8693f220d9fe16a484d30c05ae5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b326414a9ce8d9cfb564b3b4debef71e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1cd0a3a65c61b708a21b922278ad8491_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b40742ccc8369c58f08577a0fb0b39a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"90\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ca6e099f51574f07c2c415677347a28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"89\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e8db5a73d8dbae61a2f3a063b73a661b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"89\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-943ecae62f54f330237d83fcad4f282e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"89\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b37c0dcff66f7a836d76a4680e3137c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8eb64b3c57d9d80fe0e48f97bc9aff70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#52;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-82a092214ecc5da44cf9990d699b68a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;&#46;&#49;&#120;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-82a092214ecc5da44cf9990d699b68a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;&#46;&#49;&#120;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596394458\">Choose the Most Convenient Method to Graph a Line<\/h2>\n<p id=\"fs-id1169596394464\">In the following exercises, determine the most convenient method to graph each line.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 51.0055%;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0621c4f761e7864714642fcc62d4c42f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 48.9945%;\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.0055%;\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e135cd6350a4c21195c621240f7aee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 48.9945%;\">36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-39af43abd99adaf051fde7775af522c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.0055%;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-78f61cfc28f5faaecd05d59f13a23113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 48.9945%;\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-78f61cfc28f5faaecd05d59f13a23113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.0055%;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cd3280b6ac04411312aa3a6fb0b11632_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 48.9945%;\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f246c694f3d64b7ca3b620ac0c2bac11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.0055%;\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6251b9fc3ad2f5b1a38018d04f34960a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 48.9945%;\">42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-56977bb9bf99835acf4e5c84148ac24d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.0055%;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9f371b4e77462e28d9f6119571c92982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 48.9945%;\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-91f9ec631e44f3d108457c2f8adad27c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.0055%;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-36df0dbd210fef0a71a117cadf263abc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#53;&#121;&#61;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"114\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 48.9945%;\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cd87f7018f9e0374daed03243f8543a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#50;&#121;&#61;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"113\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.0055%;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4d32b8c4ad0824693226cb91a0a03640_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"99\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 48.9945%;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0a2744ab1028469dbe970bd35237c0c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"90\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596696889\">Graph and Interpret Applications of Slope\u2013Intercept<\/h2>\n<table style=\"border-collapse: collapse; width: 100%; height: 894px;\">\n<tbody>\n<tr>\n<td style=\"width: 48.0804%;\">\n<p id=\"fs-id1169594137524\">49. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e683eba35c410a1f6145bdcbc226f660_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#50;&#56;&#43;&#50;&#46;&#53;&#52;&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"122\" style=\"vertical-align: -2px;\" \/> models the relation between the amount of Randy\u2019s monthly water bill payment, <em data-effect=\"italics\">P<\/em>, in dollars, and the number of units of water, <em data-effect=\"italics\">w<\/em>, used.<\/p>\n<ol id=\"fs-id1169595115415\" class=\"circled\" type=\"a\">\n<li>Find the payment for a month when Randy used 0 units of water.<\/li>\n<li>Find the payment for a month when Randy used 15 units of water.<\/li>\n<li>Interpret the slope and <em data-effect=\"italics\">P<\/em>-intercept of the equation.<\/li>\n<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 51.9196%;\">\n<p id=\"fs-id1169596696900\">50. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-df8178ff75200a1bc53136bee37eb4a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#51;&#49;&#43;&#49;&#46;&#55;&#53;&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"122\" style=\"vertical-align: -2px;\" \/> models the relation between the amount of Tuyet\u2019s monthly water bill payment, <em data-effect=\"italics\">P<\/em>, in dollars, and the number of units of water, <em data-effect=\"italics\">w<\/em>, used.<\/p>\n<ol id=\"fs-id1169595184692\" class=\"circled\" type=\"a\">\n<li>Find Tuyet\u2019s payment for a month when 0 units of water are used.<\/li>\n<li>Find Tuyet\u2019s payment for a month when 12 units of water are used.<\/li>\n<li>Interpret the slope and <em data-effect=\"italics\">P<\/em>-intercept of the equation.<\/li>\n<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.0804%;\">\n<p id=\"fs-id1169596446176\">51. Janelle is planning to rent a car while on vacation. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7d070b50e8f0f1d6f60e5cdd8bacef2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#48;&#46;&#51;&#50;&#109;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"123\" style=\"vertical-align: -2px;\" \/> models the relation between the cost in dollars, <em data-effect=\"italics\">C<\/em>, per day and the number of miles, <em data-effect=\"italics\">m<\/em>, she drives in one day.<\/p>\n<ol id=\"fs-id1169595585090\" class=\"circled\" type=\"a\">\n<li>Find the cost if Janelle drives the car 0 miles one day.<\/li>\n<li>Find the cost on a day when Janelle drives the car 400 miles.<\/li>\n<li>Interpret the slope and <em data-effect=\"italics\">C<\/em>\u2013intercept of the equation.<\/li>\n<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 51.9196%;\">\n<p id=\"fs-id1169596446433\">52. Bruce drives his car for his job. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b4f77bc2d461f3fcfc3eca65b3e4a321_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#61;&#48;&#46;&#53;&#55;&#53;&#109;&#43;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"132\" style=\"vertical-align: -2px;\" \/> models the relation between the amount in dollars, <em data-effect=\"italics\">R<\/em>, that he is reimbursed and the number of miles, <em data-effect=\"italics\">m<\/em>, he drives in one day.<\/p>\n<ol id=\"fs-id1169595196976\" class=\"circled\" type=\"a\">\n<li>Find the amount Bruce is reimbursed on a day when he drives 0 miles.<\/li>\n<li>Find the amount Bruce is reimbursed on a day when he drives 220 miles.<\/li>\n<li>Interpret the slope and <em data-effect=\"italics\">R<\/em>-intercept of the equation.<\/li>\n<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.0804%;\">\n<p id=\"fs-id1169596445597\">53. Patel\u2019s weekly salary includes a base pay plus commission on his sales. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8da13de69ced05659596c15ee07e42db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#55;&#53;&#48;&#43;&#48;&#46;&#48;&#57;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"124\" style=\"vertical-align: -2px;\" \/> models the relation between his weekly salary, <em data-effect=\"italics\">S<\/em>, in dollars and the amount of his sales, <em data-effect=\"italics\">c<\/em>, in dollars.<\/p>\n<ol id=\"fs-id1169595585924\" class=\"circled\" type=\"a\">\n<li>Find Patel\u2019s salary for a week when his sales were 0.<\/li>\n<li>Find Patel\u2019s salary for a week when his sales were 18,540.<\/li>\n<li>Interpret the slope and <em data-effect=\"italics\">S<\/em>-intercept of the equation.<\/li>\n<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 51.9196%;\">\n<p id=\"fs-id1169596649003\">54. Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6173ec2d342ee8a5fee855079adb11d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#52;&#48;&#48;&#43;&#48;&#46;&#49;&#53;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"124\" style=\"vertical-align: -2px;\" \/> models the relation between her weekly salary, <em data-effect=\"italics\">S<\/em>, in dollars and the amount of her sales, <em data-effect=\"italics\">c<\/em>, in dollars.<\/p>\n<ol id=\"fs-id1169595278333\" class=\"circled\" type=\"a\">\n<li>Find Cherie\u2019s salary for a week when her sales were 0.<\/li>\n<li>Find Cherie\u2019s salary for a week when her sales were 3600.<\/li>\n<li>Interpret the slope and <em data-effect=\"italics\">S<\/em>\u2013intercept of the equation.<\/li>\n<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.0804%;\">\n<p id=\"fs-id1169594041745\">55. Margie is planning a dinner banquet. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-024f740658874f1fbf313875b37177a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#55;&#53;&#48;&#43;&#52;&#50;&#103;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"113\" style=\"vertical-align: -4px;\" \/> models the relation between the cost in dollars, <em data-effect=\"italics\">C<\/em> of the banquet and the number of guests, <em data-effect=\"italics\">g<\/em>.<\/p>\n<ol id=\"fs-id1169597725768\" class=\"circled\" type=\"a\">\n<li>Find the cost if the number of guests is 50.<\/li>\n<li>Find the cost if the number of guests is 100.<\/li>\n<li>Interpret the slope and <em data-effect=\"italics\">C<\/em>\u2013intercept of the equation.<\/li>\n<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 51.9196%;\">\n<p id=\"fs-id1169596697130\">56. Costa is planning a lunch banquet. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b54f7964bd07875926f04eb2d2f4411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#52;&#53;&#48;&#43;&#50;&#56;&#103;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"113\" style=\"vertical-align: -4px;\" \/> models the relation between the cost in dollars, <em data-effect=\"italics\">C<\/em>, of the banquet and the number of guests, <em data-effect=\"italics\">g<\/em>.<\/p>\n<ol id=\"fs-id1169595584374\" class=\"circled\" type=\"a\">\n<li>Find the cost if the number of guests is 40.<\/li>\n<li>Find the cost if the number of guests is 80.<\/li>\n<li>Interpret the slope and <em data-effect=\"italics\">C<\/em>-intercept of the equation.<\/li>\n<li>Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596636338\">Use Slopes to Identify Parallel Lines<\/h2>\n<p id=\"fs-id1169596636344\">In the following exercises, use slopes and y-intercepts to determine if the lines are parallel.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 200px;\">\n<tbody>\n<tr>\n<td style=\"width: 48.4461%;\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d4850ca7cd5ccd61c99a16c9d3ffee46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#120;&#45;&#49;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#120;&#45;&#51;&#121;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"208\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 51.3711%;\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7a0cdc8c1c37888660fdf39d6f1a56e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#45;&#51;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#120;&#45;&#52;&#121;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"208\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c9365a07351dc0e0870c846c9f9b30d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#52;&#121;&#61;&#45;&#50;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#45;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"208\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 51.3711%;\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1e213f59c82b2e4c4c435dc3162b64a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#53;&#121;&#61;&#45;&#51;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#120;&#43;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"207\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a542ab9ec636a2b9751361e24d07d159_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#45;&#51;&#121;&#61;&#57;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#120;&#45;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.3711%;\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b84c9496ab982d5c47f7767c2a649a86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#52;&#121;&#61;&#54;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#50;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-58f24f41995f13d49066c839942d965a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#43;&#54;&#121;&#61;&#54;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#50;&#120;&#43;&#57;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"216\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.3711%;\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-acfee836c5dd64ab8b324f200eb6a6c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#50;&#121;&#61;&#54;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#54;&#120;&#43;&#51;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"200\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0d6fdfb2555ce5607578d41da27372e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#55;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"116\" style=\"vertical-align: -3px;\" \/><\/td>\n<td style=\"width: 51.3711%;\">66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-963a18c77d86f6c034597308cd6e9bfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"116\" style=\"vertical-align: -3px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-12250edb4c0995fab5dab62ba2506742_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"129\" style=\"vertical-align: -3px;\" \/><\/td>\n<td style=\"width: 51.3711%;\">68. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d2c25dd949c9e2e76bea7ccb061a49e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#52;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"129\" style=\"vertical-align: -3px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a1414a90a232554b3447b93a5eeb822f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.3711%;\">70. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f094ebc314174884f0a98e2ed07c247f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"101\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">71. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4fd38abf3975b561733ffdec19d06990_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#49;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"113\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.3711%;\">72. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a577eb1ef59708ec02a689b562f84713_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"114\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">73. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5874b0f4972b44a1d9daff76b392d14b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#52;&#121;&#61;&#56;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#43;&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"181\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.3711%;\">74. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-16d3a88ff74e76a9a43109fc32961ade_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#61;&#50;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#120;&#45;&#50;&#121;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"182\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c90f99fbc06a53fbfc1d52d0a02336bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#45;&#50;&#121;&#61;&#49;&#49;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#120;&#45;&#121;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"200\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.3711%;\">76. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-840d808515c801754654f69c6186a470_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#51;&#121;&#61;&#54;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#120;&#45;&#54;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"199\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">77. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9185a46a5859dc5cd9a3bf7fea42667a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#56;&#121;&#61;&#49;&#54;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#50;&#121;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"200\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.3711%;\">78. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e3a89eb70d8923c35be27844a380a318_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#54;&#121;&#61;&#49;&#50;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#54;&#120;&#45;&#51;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"208\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">79. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b222fc061039afec382e605ec178b76c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#53;&#121;&#61;&#49;&#48;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#120;&#45;&#121;&#61;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"214\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.3711%;\">80. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-935b20428b8c8f62b0f42d8937c0bb59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;&#45;&#51;&#121;&#61;&#54;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#120;&#45;&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"190\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">81. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3b7e868a283f48770769db3d8dafc5ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;&#45;&#53;&#121;&#61;&#52;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#120;&#43;&#57;&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"213\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.3711%;\">82. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9ae6364c5d0f7947bc594ed69ba57e83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#45;&#52;&#121;&#61;&#56;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#120;&#43;&#55;&#121;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"209\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596649210\">Use Slopes to Identify Perpendicular Lines<\/h2>\n<p id=\"fs-id1169596649216\">In the following exercises, use slopes and y-intercepts to determine if the lines are perpendicular.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\">\n<tbody>\n<tr>\n<td style=\"width: 49.9086%;\">83. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-810c9670d4991b6b13e5d377e72f4e36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#52;&#121;&#61;&#56;&#59;&#52;&#120;&#43;&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"172\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">84. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-58888211b536cd98d87dfb4b429b5c37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#50;&#121;&#61;&#56;&#59;&#50;&#120;&#43;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">85. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b502073d7b1ce648290f8df27a197459_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#51;&#121;&#61;&#53;&#59;&#51;&#120;&#45;&#50;&#121;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">86. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a2c6a282cb3c94843a2f8987f42eca1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#53;&#121;&#61;&#51;&#59;&#53;&#120;&#45;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">87. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2d58672484b8175442055156635937ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#52;&#121;&#61;&#56;&#59;&#52;&#120;&#45;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">88. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ab39840e5810101da53d92996b2c225_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#50;&#121;&#61;&#49;&#59;&#50;&#120;&#45;&#51;&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"190\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">89. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-65d215c526c831c6549a9c8984bc7d78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#52;&#121;&#61;&#51;&#59;&#54;&#120;&#43;&#51;&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"190\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">90. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3182dccc253d59e3445360db0075378_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#43;&#50;&#121;&#61;&#54;&#59;&#50;&#120;&#43;&#53;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">91. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a431a6247f391c525c22294230dfdaf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#54;&#121;&#61;&#52;&#59;&#49;&#50;&#120;&#43;&#52;&#121;&#61;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"200\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">92. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d4c0d9f9ef3ee88f1d11a0a257c54fa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#50;&#121;&#61;&#53;&#59;&#51;&#120;&#43;&#54;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">93. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a2eb061845a4e0311dc49c2841c73dc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#45;&#50;&#121;&#61;&#55;&#59;&#51;&#120;&#43;&#49;&#50;&#121;&#61;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"200\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">94. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2413c3df5dc5c48b5f22e9f25773d144_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#45;&#52;&#121;&#61;&#53;&#59;&#56;&#120;&#43;&#49;&#50;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"200\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 49.7258%;\">\n<p id=\"fs-id1169594045888\">95. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b994794c5763523e993bbbcccc02c0ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#52;&#84;&#45;&#49;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"105\" style=\"vertical-align: -1px;\" \/> is used to estimate the number of cricket chirps, <em data-effect=\"italics\">n<\/em>, in one minute based on the temperature in degrees Fahrenheit, <em data-effect=\"italics\">T<\/em>.<\/p>\n<ol id=\"fs-id1169597838426\" class=\"circled\" type=\"a\">\n<li>Explain what the slope of the equation means.<\/li>\n<li>Explain what the <em data-effect=\"italics\">n<\/em>\u2013intercept of the equation means. Is this a realistic situation?<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 50.2742%;\">\n<p id=\"fs-id1169596696823\">96. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bc580b75223e81e579d682bbcc1b2408_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#57;&#125;&#70;&#45;&#49;&#55;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"118\" style=\"vertical-align: -12px;\" \/> can be used to convert temperatures <em data-effect=\"italics\">F<\/em>, on the Fahrenheit scale to temperatures, <em data-effect=\"italics\">C<\/em>, on the Celsius scale.<\/p>\n<ol id=\"fs-id1169595484565\" class=\"circled\" type=\"a\">\n<li>Explain what the slope of the equation means.<\/li>\n<li>Explain what the <em data-effect=\"italics\">C<\/em>\u2013intercept of the equation means.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">97. Why are all horizontal lines parallel?<\/td>\n<td style=\"width: 50.2742%;\">98. Explain in your own words how to decide which method to use to graph a line.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 1424px;\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">2. slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e5072b7479ca854c5e3cdea8ffff2c0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: -1px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3ecef9f206503704c74407265b403ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">3. slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-53a904699623d35001768f429bb03314_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"62\" style=\"vertical-align: 0px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-99d11505e9b59f8e2d3351529e3354c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">6. slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8cd6975e33735ed1061f5783198c10e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"64\" style=\"vertical-align: -12px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef24d382319a3ce81f280194edba003a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27a3f53594a2df015156a8017542f20f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"68\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ded457bdaf698a8020cf942ac7997557_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f745873d09b5a3fad19a0906e04825c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"68\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5126ff1a6272c61ae5699b6f5e312caf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#51;&#125;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"72\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-64e4114485e2cec3769dab11ff253f20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#51;&#125;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"71\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 288px;\">\n<td style=\"width: 50%; height: 288px;\">18.<\/p>\n<p><span id=\"fs-id1169596756240\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 4) and (1, 5).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_208_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 4) and (1, 5).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%; height: 288px;\">19.<\/p>\n<p><span id=\"fs-id1169596649307\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (1, negative 1).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_210_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (1, negative 1).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 288px;\">\n<td style=\"width: 50%; height: 288px;\">22.<\/p>\n<p><span id=\"fs-id1169596648488\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 3) and (1, 2).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_212_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 3) and (1, 2).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%; height: 288px;\">23.<\/p>\n<p><span id=\"fs-id1169594008358\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1, negative 3).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_214_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1, negative 3).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 288px;\">\n<td style=\"width: 50%; height: 288px;\">26.<\/p>\n<p><span id=\"fs-id1169596383013\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (5, negative 5).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_216_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (5, negative 5).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%; height: 288px;\">27.<\/p>\n<p><span id=\"fs-id1169596516339\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 1).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_218_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 1).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 288px;\">\n<td style=\"width: 50%; height: 288px;\">30.<\/p>\n<p><span id=\"fs-id1169594004625\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (3,2).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_220_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (3,2).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%; height: 288px;\">31.<\/p>\n<p><span id=\"fs-id1169596529660\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 25) and (negative 50, 10).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_222_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 25) and (negative 50, 10).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">34. horizontal line<\/td>\n<td style=\"width: 50%; height: 16px;\">35. vertical line<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">38. slope\u2013intercept<\/td>\n<td style=\"width: 50%; height: 16px;\">39. intercepts<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">42. slope\u2013intercept<\/td>\n<td style=\"width: 50%; height: 16px;\">43. horizontal line<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">46. intercepts<\/td>\n<td style=\"width: 50%; height: 16px;\">47. slope\u2013intercept<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">50.<\/p>\n<div id=\"fs-id1169594137574\" data-type=\"solution\">\n<p>a) &#36;28<\/p>\n<p>b) &#36;66.10<\/p>\n<p>c) The slope, 2.54, means that Randy\u2019s payment, <em data-effect=\"italics\">P<\/em>, increases by &#36;2.54 when the number of units of water he used, <em data-effect=\"italics\">w,<\/em> increases by 1. The <em data-effect=\"italics\">P<\/em>\u2013intercept means that if the number units of water Randy used was 0, the payment would be &#36;28.<\/p>\n<p>d)<br \/>\n<span id=\"fs-id1169596446413\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 2 to 20. The y-axis of the plane represents the variable P and runs from negative 1 to 100. The line begins at the point (0, 28) and goes through the point (15, 66.1).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_224_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 2 to 20. The y-axis of the plane represents the variable P and runs from negative 1 to 100. The line begins at the point (0, 28) and goes through the point (15, 66.1).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/td>\n<td style=\"width: 50%; height: 16px;\">51.<\/p>\n<div id=\"fs-id1169596648954\" data-type=\"solution\">\n<p>a) &#36;15<\/p>\n<p>b) &#36;143<\/p>\n<p>c) The slope, 0.32, means that the cost, <em data-effect=\"italics\">C<\/em>, increases by &#36;0.32 when the number of miles driven, <em data-effect=\"italics\">m,<\/em> increases by 1. The <em data-effect=\"italics\">C<\/em>-intercept means that if Janelle drives 0 miles one day, the cost would be &#36;15.<\/p>\n<p>d)<br \/>\n<span id=\"fs-id1169596648983\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 1 to 500. The y-axis of the plane represents the variable C and runs from negative 1 to 200. The line begins at the point (0,15) and goes through the point (400,143).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_226_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 1 to 500. The y-axis of the plane represents the variable C and runs from negative 1 to 200. The line begins at the point (0,15) and goes through the point (400,143).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">54.<\/p>\n<div id=\"fs-id1169596697088\" data-type=\"solution\">\n<p>a) &#36;750<\/p>\n<p>b) &#36;2418.60<\/p>\n<p>c) The slope, 0.09, means that Patel\u2019s salary, <em data-effect=\"italics\">S<\/em>, increases by &#36;0.09 for every &#36;1 increase in his sales. The <em data-effect=\"italics\">S<\/em>-intercept means that when his sales are &#36;0, his salary is &#36;750.<\/p>\n<p>d)<br \/>\n<span id=\"fs-id1169596697110\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 1 to 20000. The y-axis of the plane represents the variable P and runs from negative 1 to 3000. The line begins at the point (0, 750) and goes through the point (18540, 2415).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_228_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 1 to 20000. The y-axis of the plane represents the variable P and runs from negative 1 to 3000. The line begins at the point (0, 750) and goes through the point (18540, 2415).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/td>\n<td style=\"width: 50%; height: 16px;\">55.<\/p>\n<div id=\"fs-id1169596636299\" data-type=\"solution\">\n<p>a) &#36;2850<\/p>\n<p>b) &#36;4950<\/p>\n<p>c) The slope, 42, means that the cost, <em data-effect=\"italics\">C<\/em>, increases by &#36;42 for when the number of guests increases by 1. The <em data-effect=\"italics\">C<\/em>-intercept means that when the number of guests is 0, the cost would be &#36;750.<\/p>\n<p>d)<br \/>\n<span id=\"fs-id1169596636321\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable g and runs from negative 1 to 150. The y-axis of the plane represents the variable C and runs from negative 1 to 7000. The line begins at the point (0, 750) and goes through the point (100, 4950).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_230_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable g and runs from negative 1 to 150. The y-axis of the plane represents the variable C and runs from negative 1 to 7000. The line begins at the point (0, 750) and goes through the point (100, 4950).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">58. parallel<\/td>\n<td style=\"width: 50%; height: 16px;\">59. parallel<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">62.\u00a0parallel<\/td>\n<td style=\"width: 50%; height: 16px;\">63. parallel<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">66. parallel<\/td>\n<td style=\"width: 50%; height: 16px;\">67. parallel<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">70. parallel<\/td>\n<td style=\"width: 50%; height: 16px;\">71. parallel<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">74. not parallel<\/td>\n<td style=\"width: 50%; height: 16px;\">75. not parallel<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">78. not parallel<\/td>\n<td style=\"width: 50%; height: 16px;\">79. not parallel<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">82. not parallel<\/td>\n<td style=\"width: 50%; height: 16px;\">83. perpendicular<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">86. perpendicular<\/td>\n<td style=\"width: 50%;\">87. not perpendicular<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">90. not perpendicular<\/td>\n<td style=\"width: 50%;\">91. perpendicular<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">94. perpendicular<\/td>\n<td style=\"width: 50%;\">95.<\/p>\n<p>a) For every increase of one degree Fahrenheit, the number of chirps increases by four.<\/p>\n<div id=\"fs-id1169594045932\" data-type=\"solution\">\n<p>b) There would be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d5f41eb3c28c97ce3a9ae75eabb353d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/> chirps when the Fahrenheit temperature is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>\u00b0. (Notice that this does not make sense; this model cannot be used for all possible temperatures.)<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">98. Answers will vary.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50.0914%;\">1. slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e5072b7479ca854c5e3cdea8ffff2c0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: -1px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3ecef9f206503704c74407265b403ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">3. slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-53a904699623d35001768f429bb03314_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"62\" style=\"vertical-align: 0px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-99d11505e9b59f8e2d3351529e3354c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">5. slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8cd6975e33735ed1061f5783198c10e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"64\" style=\"vertical-align: -12px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef24d382319a3ce81f280194edba003a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27a3f53594a2df015156a8017542f20f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"68\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ded457bdaf698a8020cf942ac7997557_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f745873d09b5a3fad19a0906e04825c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"68\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5126ff1a6272c61ae5699b6f5e312caf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#51;&#125;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"72\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-64e4114485e2cec3769dab11ff253f20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#51;&#125;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"71\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">17.<\/p>\n<p><span id=\"fs-id1169596756240\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 4) and (1, 5).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_208_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 4) and (1, 5).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.9086%;\">19.<\/p>\n<p><span id=\"fs-id1169596649307\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (1, negative 1).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_210_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (1, negative 1).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">21.<\/p>\n<p><span id=\"fs-id1169596648488\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 3) and (1, 2).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_212_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 3) and (1, 2).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.9086%;\">23.<\/p>\n<p><span id=\"fs-id1169594008358\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1, negative 3).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_214_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1, negative 3).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">25.<\/p>\n<p><span id=\"fs-id1169596383013\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (5, negative 5).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_216_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (5, negative 5).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.9086%;\">27.<\/p>\n<p><span id=\"fs-id1169596516339\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 1).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_218_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 1).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">29.<\/p>\n<p><span id=\"fs-id1169594004625\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (3,2).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_220_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (3,2).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.9086%;\">31.<\/p>\n<p><span id=\"fs-id1169596529660\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 25) and (negative 50, 10).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_222_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 25) and (negative 50, 10).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">33. horizontal line<\/td>\n<td style=\"width: 49.9086%;\">35. vertical line<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">37. slope\u2013intercept<\/td>\n<td style=\"width: 49.9086%;\">39. intercepts<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">41. slope\u2013intercept<\/td>\n<td style=\"width: 49.9086%;\">43. horizontal line<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">45. intercepts<\/td>\n<td style=\"width: 49.9086%;\">47. slope\u2013intercept<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">49.<\/p>\n<div id=\"fs-id1169594137574\" data-type=\"solution\">\n<p>a) &#36;28<\/p>\n<p>b) &#36;66.10<\/p>\n<p>c) The slope, 2.54, means that Randy\u2019s payment, <em data-effect=\"italics\">P<\/em>, increases by &#36;2.54 when the number of units of water he used, <em data-effect=\"italics\">w,<\/em> increases by 1. The <em data-effect=\"italics\">P<\/em>\u2013intercept means that if the number units of water Randy used was 0, the payment would be &#36;28.<\/p>\n<p>d)<br \/>\n<span id=\"fs-id1169596446413\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 2 to 20. The y-axis of the plane represents the variable P and runs from negative 1 to 100. The line begins at the point (0, 28) and goes through the point (15, 66.1).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_224_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 2 to 20. The y-axis of the plane represents the variable P and runs from negative 1 to 100. The line begins at the point (0, 28) and goes through the point (15, 66.1).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/td>\n<td style=\"width: 49.9086%;\">51.<\/p>\n<div id=\"fs-id1169596648954\" data-type=\"solution\">\n<p>a) &#36;15<\/p>\n<p>b) &#36;143<\/p>\n<p>c) The slope, 0.32, means that the cost, <em data-effect=\"italics\">C<\/em>, increases by &#36;0.32 when the number of miles driven, <em data-effect=\"italics\">m,<\/em> increases by 1. The <em data-effect=\"italics\">C<\/em>-intercept means that if Janelle drives 0 miles one day, the cost would be &#36;15.<\/p>\n<p>d)<br \/>\n<span id=\"fs-id1169596648983\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 1 to 500. The y-axis of the plane represents the variable C and runs from negative 1 to 200. The line begins at the point (0,15) and goes through the point (400,143).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_226_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 1 to 500. The y-axis of the plane represents the variable C and runs from negative 1 to 200. The line begins at the point (0,15) and goes through the point (400,143).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">53.<\/p>\n<div id=\"fs-id1169596697088\" data-type=\"solution\">\n<p>a) &#36;750<\/p>\n<p>b) &#36;2418.60<\/p>\n<p>c) The slope, 0.09, means that Patel\u2019s salary, <em data-effect=\"italics\">S<\/em>, increases by &#36;0.09 for every &#36;1 increase in his sales. The <em data-effect=\"italics\">S<\/em>-intercept means that when his sales are &#36;0, his salary is &#36;750.<\/p>\n<p>d)<br \/>\n<span id=\"fs-id1169596697110\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 1 to 20000. The y-axis of the plane represents the variable P and runs from negative 1 to 3000. The line begins at the point (0, 750) and goes through the point (18540, 2415).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_228_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 1 to 20000. The y-axis of the plane represents the variable P and runs from negative 1 to 3000. The line begins at the point (0, 750) and goes through the point (18540, 2415).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/td>\n<td style=\"width: 49.9086%;\">55.<\/p>\n<div id=\"fs-id1169596636299\" data-type=\"solution\">\n<p>a) &#36;2850<\/p>\n<p>b) &#36;4950<\/p>\n<p>c) The slope, 42, means that the cost, <em data-effect=\"italics\">C<\/em>, increases by &#36;42 for when the number of guests increases by 1. The <em data-effect=\"italics\">C<\/em>-intercept means that when the number of guests is 0, the cost would be &#36;750.<\/p>\n<p>d)<br \/>\n<span id=\"fs-id1169596636321\" data-type=\"media\" data-alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable g and runs from negative 1 to 150. The y-axis of the plane represents the variable C and runs from negative 1 to 7000. The line begins at the point (0, 750) and goes through the point (100, 4950).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_05_230_img_new.jpg\" alt=\"The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable g and runs from negative 1 to 150. The y-axis of the plane represents the variable C and runs from negative 1 to 7000. The line begins at the point (0, 750) and goes through the point (100, 4950).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">57. parallel<\/td>\n<td style=\"width: 49.9086%;\">59. parallel<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">61. parallel<\/td>\n<td style=\"width: 49.9086%;\">63. parallel<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">65. parallel<\/td>\n<td style=\"width: 49.9086%;\">67. parallel<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">69. parallel<\/td>\n<td style=\"width: 49.9086%;\">71. parallel<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">73. not parallel<\/td>\n<td style=\"width: 49.9086%;\">75. not parallel<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">77. not parallel<\/td>\n<td style=\"width: 49.9086%;\">79. not parallel<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">81. not parallel<\/td>\n<td style=\"width: 49.9086%;\">83. perpendicular<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">85. perpendicular<\/td>\n<td style=\"width: 49.9086%;\">87. not perpendicular<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">89. not perpendicular<\/td>\n<td style=\"width: 49.9086%;\">91. perpendicular<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">93. perpendicular<\/td>\n<td style=\"width: 49.9086%;\">95.<\/p>\n<p>a) For every increase of one degree Fahrenheit, the number of chirps increases by four.<\/p>\n<div id=\"fs-id1169594045932\" data-type=\"solution\">\n<p>b) There would be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d5f41eb3c28c97ce3a9ae75eabb353d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/> chirps when the Fahrenheit temperature is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>\u00b0. (Notice that this does not make sense; this model cannot be used for all possible temperatures.)<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">97. Answers will vary.<\/td>\n<td style=\"width: 49.9086%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cUse the Slope\u2013Intercept Form of an Equation of a Line\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n","protected":false},"author":90,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1775","chapter","type-chapter","status-publish","hentry"],"part":1370,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1775","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1775\/revisions"}],"predecessor-version":[{"id":1776,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1775\/revisions\/1776"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/1370"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1775\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=1775"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1775"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=1775"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=1775"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}