{"id":1844,"date":"2020-07-31T20:35:58","date_gmt":"2020-08-01T00:35:58","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/find-the-equation-of-a-line\/"},"modified":"2025-09-16T14:25:43","modified_gmt":"2025-09-16T18:25:43","slug":"find-the-equation-of-a-line","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/find-the-equation-of-a-line\/","title":{"raw":"6.6 Find the Equation of a Line","rendered":"6.6 Find the 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>Find an equation of the line given the slope and \\(y\\)-intercept<\/li>\n \t<li>Find an equation of the line given the slope and a point<\/li>\n \t<li>Find an equation of the line given two points<\/li>\n \t<li>Find an equation of a line parallel to a given line<\/li>\n \t<li>Find an equation of a line perpendicular to a given line<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596399867\">How do online retailers know that \u2018you may also like\u2019 a particular item based on something you just ordered? How can economists know how a rise in the minimum wage will affect the unemployment rate? How do medical researchers create drugs to target cancer cells? How can traffic engineers predict the effect on your commuting time of an increase or decrease in gas prices? It\u2019s all mathematics.<\/p>\n<p id=\"fs-id1169594212431\">You are at an exciting point in your mathematical journey as the mathematics you are studying has interesting applications in the real world.<\/p>\n<p id=\"fs-id1169596387304\">The physical sciences, social sciences, and the business world are full of situations that can be modeled with linear equations relating two variables. Data is collected and graphed. If the data points appear to form a straight line, an equation of that line can be used to predict the value of one variable based on the value of the other variable.<\/p>\n<p id=\"fs-id1169596687875\">To create a mathematical model of a linear relation between two variables, we must be able to find the equation of the line. In this section we will look at several ways to write the equation of a line. The specific method we use will be determined by what information we are given.<\/p>\n\n<h1>Find an Equation of the Line Given the Slope and y-Intercept<\/h1>\n<p id=\"fs-id1169596256506\">We can easily determine the slope and intercept of a line if the equation was written in slope\u2013intercept form, \\(y=mx+b\\). Now, we will do the reverse\u2014we will start with the slope and <em data-effect=\"italics\">y<\/em>-intercept and use them to find the equation of the line.<\/p>\n\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-id1169596370489\" data-type=\"problem\">\n\nFind an equation of a line with slope \\(-7\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-1\\right)\\).\n\n<\/div>\n<div id=\"fs-id1169594154667\" 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-id1169596619558\">Since we are given the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line, we can substitute the needed values into the slope\u2013intercept form, \\(y=mx+b\\).<\/p>\n\n<table id=\"eip-id1172183502249\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the top row, the instructions in the left column say \u201cName the slope.\u201d In the right column is m equals negative 7. One row down, the instructions in the left column say \u201cName the y-intercept.\u201d In the right column is the y-intercept defined as the ordered pair (0, negative 1). One row down, the instructions in the left column say \u201cSubstitute the values into y equals mx plus b.\u201d In the right column is the slope-intercept form: y equals mx plus b. Below this is the formula with negative 7 substituted for m and negative 1 substituted for b: y equals negative 7x plus negative 1. Below this is the formula simplified: y equals negative 7x minus 1.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Name the slope.<\/td>\n<td><span id=\"eip-id1172184381083\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/07\/CNX_ElemAlg_Figure_04_06_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Name the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td><span id=\"eip-id1172187819874\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute the values into \\(y=mx+b\\).<\/td>\n<td><span id=\"eip-id1172183461192\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172177957049\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_008d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172184642450\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_008e_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 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596237406\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169596448823\">Find an equation of a line with slope \\(\\dfrac{2}{5}\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,4\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596241029\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596689594\">\\(y=\\dfrac{2}{5}x+4\\)<\/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 data-type=\"problem\">\n<p id=\"fs-id1169594011554\">Find an equation of a line with slope \\(-1\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-3\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596623578\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596567679\">\\(y=-x-3\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596765935\">Sometimes, the slope and intercept need to be determined from the graph.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE\u00a0 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596395488\" data-type=\"problem\">\n<p id=\"fs-id1169596219194\">Find the equation of the line shown.<\/p>\n<span id=\"fs-id1169596299458\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. A line intercepts the y-axis at (0, negative 4), passes through the plotted point (3, negative 2), and intercepts the x-axis at (4, 0).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_001_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. A line intercepts the y-axis at (0, negative 4), passes through the plotted point (3, negative 2), and intercepts the x-axis at (4, 0).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id1169596539632\" 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-id1169594051395\">We need to find the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line from the graph so we can substitute the needed values into the slope\u2013intercept form, \\(y=mx+b\\).<\/p>\n<p id=\"fs-id1169596273127\">To find the slope, we choose two points on the graph.<\/p>\n<p id=\"fs-id1169596311636\">The <em data-effect=\"italics\">y<\/em>-intercept is \\(\\left(0,-4\\right)\\) and the graph passes through \\(\\left(3,-2\\right)\\).<\/p>\n\n<table id=\"eip-id1172185967814\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the top row, the instructions in the left column say \u201cFind the slope by counting the rise and run.\u201d In the right column is m equals rise over run. Under that is m equals two thirds. One row down, the instructions in the left column say \u201cFind the y-intercept.\u201d In the right column is the y-intercept defined as the ordered pair (0, negative 4). One row down, the instructions in the left column say \u201cSubstitute the values into y equals mx plus b.\u201d In the right column is the slope-intercept form: y equals mx plus b. Below this is the formula with negative two thirds substituted for m and negative 4 substituted for b: y equals negative two thirds x minus 4.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the slope by counting the rise and run.<\/td>\n<td><span id=\"eip-id1172185623527\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187671336\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_009b_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.<\/td>\n<td><span id=\"eip-id1172187701633\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_009c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute the values into \\(y=mx+b\\).<\/td>\n<td><span id=\"eip-id1172187191244\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_009d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172189246088\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_009e_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 id=\"fs-id1169596238261\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596387430\" data-type=\"exercise\">\n<div id=\"fs-id1169596404087\" data-type=\"problem\">\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-id1169596238261\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596387430\" data-type=\"exercise\">\n<div id=\"fs-id1169596404087\" data-type=\"problem\">\n<p id=\"fs-id1169596766107\">Find the equation of the line shown in the graph.<\/p>\n<span id=\"fs-id1169596701813\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. A line intercepts the x-axis at (negative 2, 0), intercepts the y-axis at (0, 1) and passes through the plotted point (5, 4).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_010_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. A line intercepts the x-axis at (negative 2, 0), intercepts the y-axis at (0, 1) and passes through the plotted point (5, 4).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id1169594053350\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596302685\">\\(y=\\dfrac{3}{5}x+1\\)<\/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 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596402199\" data-type=\"problem\">\n\nFind the equation of the line shown in the graph.\n\n<span id=\"fs-id1169596396794\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. A line intercepts the y-axis at (0, negative 5), passes through the plotted point (3, negative 1), and intercepts the x-axis at (15 fourths, 0).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_011_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. A line intercepts the y-axis at (0, negative 5), passes through the plotted point (3, negative 1), and intercepts the x-axis at (15 fourths, 0).\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id1169596364856\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596459716\">\\(y=\\dfrac{4}{3}x-5\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Find an Equation of the Line Given the Slope and a Point<\/h1>\n<p id=\"fs-id1169596531418\">Finding an equation of a line using the slope\u2013intercept form of the equation works well when you are given the slope and <em data-effect=\"italics\">y<\/em>-intercept or when you read them off a graph. But what happens when you have another point instead of the <em data-effect=\"italics\">y<\/em>-intercept?<\/p>\n<p id=\"fs-id1169596705156\">We are going to use the slope formula to derive another form of an equation of the line. Suppose we have a line that has slope \\(m\\) and that contains some specific point \\(\\left({x}_{1},{y}_{1}\\right)\\) and some other point, which we will just call \\(\\left(x,y\\right)\\). We can write the slope of this line and then change it to a different form.<\/p>\n\n<table id=\"eip-690\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(m=\\dfrac{y-{y}_{1}}{x-{x}_{1}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides of the equation by \\(x-{x}_{1}\\).<\/td>\n<td>\\(\\begin{array}{ccc}m\\left(x-{x}_{1}\\right)&amp; =\\hfill &amp; \\left(\\dfrac{y-{y}_{1}}{x-{x}_{1}}\\right)\\left(x-{x}_{1}\\right)\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(\\begin{array}{ccc}m\\left(x-{x}_{1}\\right)&amp; =\\hfill &amp; y-{y}_{1}\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>Rewrite the equation with the \\(y\\) terms on the left.<\/td>\n<td>\\(\\begin{array}{ccc}y-{y}_{1}&amp; =\\hfill &amp; m\\left(x-{x}_{1}\\right)\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594212615\">This format is called the point\u2013slope form of an equation of a line.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Point\u2013slope form of an equation of a line<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596239984\">The point\u2013slope form of an equation of a line with slope \\(m\\) and containing the point \\(\\left({x}_{1},{y}_{1}\\right)\\) is<\/p>\n<span id=\"fs-id1169596378255\" data-type=\"media\" data-alt=\"No alt text\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_012_img_new.jpg\" alt=\"No alt text\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<p id=\"fs-id1169596275822\">We can use the point\u2013slope form of an equation to find an equation of a line when we are given the slope and one point. Then we will rewrite the equation in slope\u2013intercept form. Most applications of linear equations use the the slope\u2013intercept form.<\/p>\n\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 data-type=\"title\">Find an Equation of a Line Given the Slope and a Point<\/div>\n<div id=\"fs-id1169596405036\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169596765661\">Find an equation of a line with slope \\(m=\\dfrac{2}{5}\\) that contains the point \\(\\left(10,3\\right)\\). Write the equation in slope\u2013intercept form.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596263363\" 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 data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Identify the slope.\u201d The text in the second cell reads: \u201cThe slope is given.\u201d The third cell contains the slope of a line, defined as m equals 2 fifths.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_016a_img_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Identify the slope.\u201d The text in the second cell reads: \u201cThe slope is given.\u201d The third cell contains the slope of a line, defined as m equals 2 fifths.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596375441\" data-type=\"media\" data-alt=\"In the second row, the first cell reads: \u201cStep 2. Identify the point.\u201d The second cell reads: \u201cThe point is given.\u201d The third cell contains the ordered pair (10, 3). A superscript x subscript 1 is written over 10, and a superscript y subscript 1 is written over 3.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_016b_img_new.jpg\" alt=\"In the second row, the first cell reads: \u201cStep 2. Identify the point.\u201d The second cell reads: \u201cThe point is given.\u201d The third cell contains the ordered pair (10, 3). A superscript x subscript 1 is written over 10, and a superscript y subscript 1 is written over 3.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596393126\" data-type=\"media\" data-alt=\"In the third row, the first cell reads: \u201cStep 3. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top line of the second cell is left blank. The third cell features the point-slope form written again: y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with 10 substituted for x subscript 1, 3 substituted for y subscript 1, and 2 fifths substituted for m: y minus 3 equals 2 fifths times x minus 10 in parentheses. One line down, the instructions in the second cell say: \u201cSimplify.\u201d In the third cell is y minus 3 equals 2 fifths x minus 4.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_016c_img_new.jpg\" alt=\"In the third row, the first cell reads: \u201cStep 3. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top line of the second cell is left blank. The third cell features the point-slope form written again: y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with 10 substituted for x subscript 1, 3 substituted for y subscript 1, and 2 fifths substituted for m: y minus 3 equals 2 fifths times x minus 10 in parentheses. One line down, the instructions in the second cell say: \u201cSimplify.\u201d In the third cell is y minus 3 equals 2 fifths x minus 4.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596308522\" data-type=\"media\" data-alt=\"In the fourth row, the first cell reads: \u201cWrite the equation in slope-intercept form.\u201d The second cell is blank. In the third cell is y equals 2 fifths x minus 1.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_016d_img_new.jpg\" alt=\"In the fourth row, the first cell reads: \u201cWrite the equation in slope-intercept form.\u201d The second cell is blank. In the third cell is y equals 2 fifths x minus 1.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596518461\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596686980\" data-type=\"exercise\">\n<div id=\"fs-id1169596522215\" data-type=\"problem\">\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-id1169596518461\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596686980\" data-type=\"exercise\">\n<div id=\"fs-id1169596522215\" data-type=\"problem\">\n<p id=\"fs-id1169596453704\">Find an equation of a line with slope \\(m=\\dfrac{5}{6}\\) and containing the point \\(\\left(6,3\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596287619\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596378552\">\\(y=\\dfrac{5}{6}x-2\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596381387\" data-type=\"exercise\">\n<div id=\"fs-id1169596238432\" data-type=\"problem\"><\/div>\n<\/div>\n<\/div>\n<\/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-id1169596238432\" data-type=\"problem\">\n\nFind an equation of a line with slope \\(m=\\dfrac{2}{3}\\) and containing thepoint \\(\\left(9,2\\right)\\).\n\n<\/div>\n<div id=\"fs-id1169594190014\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596456617\">\\(y=\\dfrac{2}{3}x-4\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596381387\" data-type=\"exercise\">\n<div id=\"fs-id1169594190014\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Find an equation of a line given the slope and a point<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol class=\"stepwise\" type=\"1\">\n \t<li>Identify the slope.<\/li>\n \t<li>Identify the point.<\/li>\n \t<li>Substitute the values into the point-slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/li>\n \t<li>Write the equation in slope\u2013intercept form.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"howto\" data-type=\"note\">\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 id=\"fs-id1169594030865\" data-type=\"problem\">\n<p id=\"fs-id1169596705433\">Find an equation of a line with slope \\(m=-\\dfrac{1}{3}\\) that contains the point \\(\\left(6,-4\\right)\\). Write the equation in slope\u2013intercept form.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596379008\" 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-id1169596421588\">Since we are given a point and the slope of the line, we can substitute the needed values into the point\u2013slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/p>\n\n<table id=\"eip-id1172186785398\" class=\"unnumbered unstyled\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the instructions in the left column read \u201cIdentify the slope.\u201d In the right column is the slope of a line defined as m equals negative 1 third. One line down, the instructions in the left column read \u201cIdentify the point.\u201d In the right column is the ordered pair (6, negative 4), with a superscript x subscript 1 above 6 and a superscript y subscript 1 above negative 4. One line down, the instructions in the left column read: \u201cSubstitute the values into y minus y subscript 1 equals m times x minus x1 in parentheses.\u201d In the right column is the point-slope form: y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with 6 substituted for x subscript 1, negative 4 substituted for y subscript 1, and negative 1 third substituted for m: y minus negative 4 equals negative 1 third times x minus 6 in parentheses. One line down, the instructions in the left column read \u201cSimplify.\u201d In the right column is y plus 4 equals 1 third x plus 2. One line down, the instructions in the left column say \u201cWrite in slope-intercept form.\u201d In the right column is y equals negative 1 third x minus 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify the slope.<\/td>\n<td><span id=\"eip-id1172182143837\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_013a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Identify the point.<\/td>\n<td><span id=\"eip-id1172185590223\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_013b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute the values into \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/td>\n<td><span id=\"eip-id1172189274612\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_013c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"fs-id1172187797821\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_013d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172186829592\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_013e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write in slope\u2013intercept form.<\/td>\n<td><span id=\"eip-id1172180357508\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_013f_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 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596581490\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596554560\" data-type=\"exercise\">\n<div id=\"fs-id1169596230637\" data-type=\"problem\">\n<p id=\"fs-id1169596463601\">Find an equation of a line with slope \\(m=-\\dfrac{2}{5}\\) and containing the point \\(\\left(10,-5\\right)\\).<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596375273\" data-type=\"solution\">\n\n\\(y=-\\dfrac{2}{5}x-1\\)\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 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594159889\" data-type=\"problem\">\n<p id=\"fs-id1169596654471\">Find an equation of a line with slope \\(m=-\\dfrac{3}{4}\\), and containing the point \\(\\left(4,-7\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596252846\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596397906\">\\(y=-\\dfrac{3}{4}x-4\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594050799\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596407606\" data-type=\"exercise\">\n<div id=\"fs-id1169596252846\" data-type=\"solution\">\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-id1169596567669\" data-type=\"problem\">\n<p id=\"fs-id1169594171652\">Find an equation of a horizontal line that contains the point \\(\\left(-1,2\\right)\\). Write the equation in slope\u2013intercept form.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596658323\" 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-id1169596690846\">Every horizontal line has slope 0. We can substitute the slope and points into the point\u2013slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/p>\n\n<table id=\"eip-id1172188999774\" class=\"unnumbered unstyled\" style=\"height: 171px;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the instructions in the left column read \u201cIdentify the slope.\u201d In the right column is the slope of a line defined as m equals 0. One line down, the instructions in the left column read \u201cIdentify the point.\u201d In the right column is the ordered pair (negative 1, 2), with a superscript x subscript 1 above negative 1 and a superscript y subscript 1 above 2. One line down, the instructions in the left column read: \u201cSubstitute the values into y minus y subscript 1 equals m times x minus x1 in parentheses.\u201d In the right column is the point-slope form: y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with negative 1 substituted for x subscript 1, 2 substituted for y subscript 1, and 0 substituted for m: y minus 2 equals 0 times x minus negative 1 in parentheses. One line down, the instructions in the left column read \u201cSimplify.\u201d In the right column is y minus 2 equals 0 times x plus 1 in parentheses. Below this is y minus 2 equals 0. Below this is y equals 2. One line down, the instructions in the left column say \u201cWrite in slope-intercept form.\u201d In the right column is the sentence: \u201cIt is in y-form, but could be written y equals 0x plus 2.\u201d\" data-label=\"\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 394.406px;\">Identify the slope.<\/td>\n<td style=\"height: 15px; width: 286.406px;\"><span id=\"fs-id1172188100755\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_014a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 39px;\">\n<td style=\"height: 39px; width: 394.406px;\">Identify the point.<\/td>\n<td style=\"height: 39px; width: 286.406px;\"><span id=\"eip-id1172189048714\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_014b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 394.406px;\">Substitute the values into \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/td>\n<td style=\"height: 19px; width: 286.406px;\"><span id=\"eip-id1172187183087\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_014c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 394.406px;\"><\/td>\n<td style=\"height: 22px; width: 286.406px;\"><span id=\"eip-id1172189038480\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_014d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 394.406px;\">Simplify.<\/td>\n<td style=\"height: 22px; width: 286.406px;\"><span id=\"eip-id1172187655483\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_014e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 394.406px;\"><\/td>\n<td style=\"height: 19px; width: 286.406px;\"><span id=\"eip-id1172179992212\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_014f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 21px;\">\n<td style=\"height: 21px; width: 394.406px;\"><\/td>\n<td style=\"height: 21px; width: 286.406px;\"><span id=\"eip-id1172187710403\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_014g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 394.406px;\">Write in slope\u2013intercept form.<\/td>\n<td style=\"height: 14px; width: 286.406px;\">It is in <em data-effect=\"italics\">y<\/em>-form, but could be written \\(y=0x+2\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596244548\">Did we end up with the form of a horizontal line, \\(y=a\\)?<\/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 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596237823\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596497043\" data-type=\"exercise\">\n<div id=\"fs-id1169596302137\" data-type=\"problem\">\n<p id=\"fs-id1169594011646\">Find an equation of a horizontal line containing the point \\(\\left(-3,8\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596441972\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596404583\">\\(y=8\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/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 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596311838\" data-type=\"problem\">\n<p id=\"fs-id1169596641169\">Find an equation of a horizontal line containing the point \\(\\left(-1,4\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596236922\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594001376\">\\(y=4\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Find an Equation of the Line Given Two Points<\/h1>\n<p id=\"fs-id1169596382559\">When real-world data is collected, a linear model can be created from two data points. In the next example we\u2019ll see how to find an equation of a line when just two points are given.<\/p>\n<p id=\"fs-id1169594031514\">We have two options so far for finding an equation of a line: slope\u2013intercept or point\u2013slope. Since we will know two points, it will make more sense to use the point\u2013slope form.<\/p>\n<p id=\"fs-id1169594171676\">But then we need the slope. Can we find the slope with just two points? Yes. Then, once we have the slope, we can use it and one of the given points to find the equation.<\/p>\n\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 data-type=\"title\">Find an Equation of a Line Given Two Points<\/div>\n<div id=\"fs-id1169596404489\" data-type=\"exercise\">\n<div id=\"fs-id1169596403384\" data-type=\"problem\">\n<p id=\"fs-id1169596685051\">Find an equation of a line that contains the points \\(\\left(5,4\\right)\\) and \\(\\left(3,6\\right)\\). Write the equation in slope\u2013intercept form.<\/p>\n\n<\/div>\n<div id=\"fs-id1169594171993\" 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-id1169596765807\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Find the slope using the given points.\u201d The text in the second cell reads: \u201cTo use the point-slope form, we first find the slope.\u201d The third cell contains the slope of a line formula: m equals y superscript 2 minus y superscript 1 divided by x superscript 2 minus x superscript 1. Below this is m equals 6 minus 4 divided by 3 minus 5. Below this is m equals 2 divided by negative 2. Below this is m equals negative 1.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_017a_img_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Find the slope using the given points.\u201d The text in the second cell reads: \u201cTo use the point-slope form, we first find the slope.\u201d The third cell contains the slope of a line formula: m equals y superscript 2 minus y superscript 1 divided by x superscript 2 minus x superscript 1. Below this is m equals 6 minus 4 divided by 3 minus 5. Below this is m equals 2 divided by negative 2. Below this is m equals negative 1.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169594096777\" data-type=\"media\" data-alt=\"In the second row, the first cell reads: \u201cStep 2. Choose one point.\u201d The second cell reads: \u201cChoose either point.\u201d The third cell contains the ordered pair (5, 4) with a superscript x subscript 1 over 5 and a superscript y subscript 1 over 4.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_017b_img_new.jpg\" alt=\"In the second row, the first cell reads: \u201cStep 2. Choose one point.\u201d The second cell reads: \u201cChoose either point.\u201d The third cell contains the ordered pair (5, 4) with a superscript x subscript 1 over 5 and a superscript y subscript 1 over 4.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596705616\" data-type=\"media\" data-alt=\"In the third row, the first cell reads: \u201cStep 3. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top line of the second cell is left blank. The third cell contains the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with 5 substituted for x subscript 1, 4 substituted for y subscript 1, and negative 1 substituted for m: y minus 4 equals negative 1 times x minus 5 in parentheses. Below this is y minus 4 equals negative x plus 5.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_017c_img_new.jpg\" alt=\"In the third row, the first cell reads: \u201cStep 3. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top line of the second cell is left blank. The third cell contains the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with 5 substituted for x subscript 1, 4 substituted for y subscript 1, and negative 1 substituted for m: y minus 4 equals negative 1 times x minus 5 in parentheses. Below this is y minus 4 equals negative x plus 5.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596641032\" data-type=\"media\" data-alt=\"In the fourth row, the first cell reads: \u201cStep 4. Write the equation in slope-intercept form.\u201d The second cell is blank. The third cell contains y equals negative x plus 9.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_017d_img_new.jpg\" alt=\"In the fourth row, the first cell reads: \u201cStep 4. Write the equation in slope-intercept form.\u201d The second cell is blank. The third cell contains y equals negative x plus 9.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596701610\">Use the point \\(\\left(3,6\\right)\\) and see that you get the same equation.<\/p>\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 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596226961\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596368188\" data-type=\"exercise\">\n<div id=\"fs-id1169596439932\" data-type=\"problem\">\n<p id=\"fs-id1169596439934\">Find an equation of a line containing the points \\(\\left(3,1\\right)\\) and \\(\\left(5,6\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596262261\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596262263\">\\(y=\\dfrac{5}{2}x-\\dfrac{13}{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594157526\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594157529\" data-type=\"exercise\">\n<div id=\"fs-id1169594054336\" data-type=\"problem\"><\/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 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594054336\" data-type=\"problem\">\n<p id=\"fs-id1169594054339\">Find an equation of a line containing the points \\(\\left(1,4\\right)\\) and \\(\\left(6,2\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596435824\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596435826\">\\(y=-\\dfrac{2}{5}x+\\dfrac{22}{5}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594157526\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594157529\" data-type=\"exercise\">\n<div id=\"fs-id1169596435824\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Find an equation of a line given two points<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169596765707\" class=\"stepwise\" type=\"1\">\n \t<li>Find the slope using the given points.<\/li>\n \t<li>Choose one point.<\/li>\n \t<li>Substitute the values into the point-slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/li>\n \t<li>Write the equation in slope\u2013intercept form.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596655632\" class=\"howto\" data-type=\"note\">\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-id1169596650155\" data-type=\"problem\">\n<p id=\"fs-id1169596399264\">Find an equation of a line that contains the points \\(\\left(-3,-1\\right)\\) and \\(\\left(2,-2\\right)\\). Write the equation in slope\u2013intercept form.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596399218\" 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-id1169594159208\">Since we have two points, we will find an equation of the line using the point\u2013slope form. The first step will be to find the slope.<\/p>\n\n<table id=\"eip-id1172185786628\" class=\"unnumbered unstyled\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the instructions in the left column say \u201cFind the slope of the line through (negative 3, negative 1) and (2, negative 2).\u201d The right column contains the slope of a line formula: m equals y superscript 2 minus y superscript 1 divided by x superscript 2 minus x superscript 1. Below this is m equals negative 2 minus negative 1 divided by 2 minus negative 3. Below this is m equals negative 1 divided by 5. Below this is m equals negative 1 fifth. One line down, the instructions on the left say \u201cChoose either point.\u201d In the right column is the ordered pair (2, negative 2) with a superscript x subscript 1 over the 2 and a superscript y subscript 1 over the negative 2. One line down, the instructions on the left say \u201cSubstitute the values into y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d In the right column is the point-slope form: y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with 2 substituted for x subscript 1, negative 2 substituted for y subscript 1, and negative 1 fifth for m: y minus negative 2 equals negative 1 fifth times x minus 2 in parentheses. Below this is y plus 2 equals negative 1 fifth x plus 2 fifths. One line down, the instructions in the left column say \u201cWrite in slope-intercept form.\u201d In the right column is y equals negative 1 fifth x minus 8 fifths.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the slope of the line through (\u22123, \u22121) and (2, \u22122).<\/td>\n<td><span id=\"eip-id1172185615472\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182398829\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172189398997\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187401152\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Choose either point.<\/td>\n<td><span id=\"eip-id1172186829636\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute the values into \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/td>\n<td><span id=\"eip-id1172187700633\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187671402\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182554715\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write in slope\u2013intercept form.<\/td>\n<td><span id=\"eip-id1172187692226\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015i_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-id1169596244226\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596244230\" data-type=\"exercise\">\n<div id=\"fs-id1169596767375\" data-type=\"problem\">\n<p id=\"fs-id1169596767378\">Find an equation of a line containing the points \\(\\left(-2,-4\\right)\\) and \\(\\left(1,-3\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596231371\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596231373\">\\(y=\\dfrac{1}{3}x-\\dfrac{10}{3}\\)<\/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 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594002070\" data-type=\"problem\">\n<p id=\"fs-id1169596691700\">Find an equation of a line containing the points \\(\\left(-4,-3\\right)\\) and \\(\\left(1,-5\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594084438\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596389137\">\\(y=-\\dfrac{2}{5}x-\\dfrac{23}{5}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594002067\" data-type=\"exercise\">\n<div id=\"fs-id1169594084438\" data-type=\"solution\">\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 data-type=\"problem\">\n<p id=\"fs-id1169596621548\">Find an equation of a line that contains the points \\(\\left(-2,4\\right)\\) and \\(\\left(-2,-3\\right)\\). Write the equation in slope\u2013intercept form.<\/p>\n\n<\/div>\n<div id=\"fs-id1169594031440\" 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-id1169594031442\">Again, the first step will be to find the slope.<\/p>\n\n<table id=\"eip-312\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Find the slope of the line through (-2,4) and (-2,-3).<\/td>\n<td>\\(m=\\dfrac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\\)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>\\(m=\\dfrac{-3-4}{-2-\\left(-2\\right)}\\)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>\\(m=\\dfrac{-7}{0}\\)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>The slope is undefined.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594178108\">This tells us it is a vertical line. Both of our points have an <em data-effect=\"italics\">x<\/em>-coordinate of \\(-2\\). So our equation of the line is \\(x=-2\\). Since there is no \\(y\\), we cannot write it in slope\u2013intercept form.<\/p>\n<p id=\"fs-id1169594049404\">You may want to sketch a graph using the two given points. Does the graph agree with our conclusion that this is a vertical 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 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596586954\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596588167\" data-type=\"exercise\">\n<div id=\"fs-id1169596588169\" data-type=\"problem\">\n<p id=\"fs-id1169596766626\">Find an equation of a line containing the points \\(\\left(5,1\\right)\\) and \\(\\left(5,-4\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596437422\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596369550\">\\(x=5\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594041658\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594041661\" data-type=\"exercise\">\n<div id=\"fs-id1169594243909\" data-type=\"problem\"><\/div>\n<\/div>\n<\/div>\n<\/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-id1169594243909\" data-type=\"problem\">\n<p id=\"fs-id1169594243911\">Find an equation of a line containing the points \\(\\left(-4,4\\right)\\) and \\(\\left(-4,3\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596252026\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596252028\">\\(x=-4\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596500442\">We have seen that we can use either the slope\u2013intercept form or the point\u2013slope form to find an equation of a line. Which form we use will depend on the information we are given. This is summarized in the following table.<\/p>\n\n<table id=\"fs-id1169596518320\" class=\"aligncenter\" summary=\"The top row of this table is a header row, which names the table: \u201cTo Write an Equation of a Line\u201d. The second row, which is also a header row, is split into three cells, and each cell names the column below it. From left to right, the first column is \u201cIf given,\u201d the second column is \u201cUse\u201d, and the third column is \u201cForm\u201d. In the third row, the \u201cIf given\u201d column contains \u2018Slope and y-intercept\u201d, the \u201cUse\u201d column contains \u201cslope-intercept\u201d, and the \u201cForm\u201d column contains the formula y equals mx plus b. In the fourth row, the \u201cIf given\u201d column contains \u201cSlope and a point\u201d, the \u201cUse\u201d column contains \u201cpoint-slope\u201d, and the \u201cForm\u201d column contains the formula y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. In the fifth row, the \u201cIf given\u201d column contains \u201cTwo points\u201d, the \u201cUse\u201d column contains \u201cpoint-slope\u201d, and the third column contains the same formula as before: y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\"><caption>To Write an Equation of a Line<\/caption>\n<tbody>\n<tr>\n<th scope=\"col\" data-valign=\"middle\" data-align=\"left\">If given:<\/th>\n<th scope=\"col\" data-valign=\"middle\" data-align=\"left\">Use:<\/th>\n<th scope=\"col\" data-valign=\"middle\" data-align=\"left\">Form:<\/th>\n<\/tr>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Slope and <em data-effect=\"italics\">y<\/em>-intercept<\/td>\n<td data-valign=\"middle\" data-align=\"left\">slope\u2013intercept<\/td>\n<td data-valign=\"middle\" data-align=\"left\">\\(y=mx+b\\)<\/td>\n<\/tr>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Slope and a point<\/td>\n<td data-valign=\"middle\" data-align=\"left\">point\u2013slope<\/td>\n<td data-valign=\"middle\" data-align=\"left\">\\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Two points<\/td>\n<td data-valign=\"middle\" data-align=\"left\">point\u2013slope<\/td>\n<td data-valign=\"middle\" data-align=\"left\">\\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1 data-type=\"title\">Find an Equation of a Line Parallel to a Given Line<\/h1>\n<p id=\"fs-id1169596373155\">Suppose we need to find an equation of a line that passes through a specific point and is parallel to a given line. We can use the fact that parallel lines have the same slope. So we will have a point and the slope\u2014just what we need to use the point\u2013slope equation.<\/p>\n<p id=\"fs-id1169594097298\">First let\u2019s look at this graphically.<\/p>\n<p id=\"fs-id1169596361007\">The graph shows the graph of \\(y=2x-3\\). We want to graph a line parallel to this line and passing through the point \\(\\left(-2,1\\right)\\).<\/p>\n<span id=\"fs-id1169596656632\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). Elsewhere on the graph, the point (negative 2, 1) is plotted.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_002_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). Elsewhere on the graph, the point (negative 2, 1) is plotted.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596377643\">We know that parallel lines have the same slope. So the second line will have the same slope as\\(y=2x-3\\). That slope is\\({m}_{\\parallel }=2\\). We\u2019ll use the notation \\({m}_{\\parallel }\\) to represent the slope of a line parallel to a line with slope \\(m\\). (Notice that the subscript \\(\\parallel \\) looks like two parallel lines.)<\/p>\n<p id=\"fs-id1169594052366\">The second line will pass through \\(\\left(-2,1\\right)\\) and have \\(m=2\\). To graph the line, we start at\\(\\left(-2,1\\right)\\) and count out the rise and run. With \\(m=2\\) (or \\(m=\\dfrac{2}{1}\\)), we count out the rise 2 and the run 1. We draw the line.<\/p>\n<span id=\"fs-id1169596288671\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). The points (negative 2, 1) and (negative 1, 3) are plotted. A second line, parallel to the first, intercepts the x-axis at (negative 5 halves, 0), passes through the points (negative 2, 1) and (negative 1, 3), and intercepts the y-axis at (0, 5).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_003_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). The points (negative 2, 1) and (negative 1, 3) are plotted. A second line, parallel to the first, intercepts the x-axis at (negative 5 halves, 0), passes through the points (negative 2, 1) and (negative 1, 3), and intercepts the y-axis at (0, 5).\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169594053849\">Do the lines appear parallel? Does the second line pass through \\(\\left(-2,1\\right)\\)?<\/p>\n<p id=\"fs-id1169594166872\">Now, let\u2019s see how to do this algebraically.<\/p>\n<p id=\"fs-id1169594166876\">We can use either the slope\u2013intercept form or the point\u2013slope form to find an equation of a line. Here we know one point and can find the slope. So we will use the point\u2013slope form.<\/p>\n\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 data-type=\"title\">How to Find an Equation of a Line Parallel to a Given Line<\/div>\n<div id=\"fs-id1169596468343\" data-type=\"exercise\">\n<div id=\"fs-id1169596468345\" data-type=\"problem\">\n<p id=\"fs-id1169596361101\">Find an equation of a line parallel to \\(y=2x-3\\) that contains the point \\(\\left(-2,1\\right)\\). Write the equation in slope\u2013intercept form.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596662604\" 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-id1169596514414\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Find the slope of the given line.\u201d The second cell reads: \u201cThe line is in slope-intercept form. y equals 2x minus 3.\u201d The third cell contains the slope of a line, defined as m equals 2.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_018a_img_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Find the slope of the given line.\u201d The second cell reads: \u201cThe line is in slope-intercept form. y equals 2x minus 3.\u201d The third cell contains the slope of a line, defined as m equals 2.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169594087301\" data-type=\"media\" data-alt=\"In the second row, the first cell reads: \u201cStep 2. Find the slope of the parallel line.\u201d The second cell reads \u201cParallel lines have the same slope.\u201d The third cell contains the slope of the parallel line, defined as m parallel equals 2.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_018b_img_new.jpg\" alt=\"In the second row, the first cell reads: \u201cStep 2. Find the slope of the parallel line.\u201d The second cell reads \u201cParallel lines have the same slope.\u201d The third cell contains the slope of the parallel line, defined as m parallel equals 2.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596634681\" data-type=\"media\" data-alt=\"In the third row, the first cell reads \u201cStep 3. Identify the point.\u201d The second cell reads \u201cThe given point is (negative 2, 1).\u201d The third cell contains the ordered pair (negative 2, 1) with a superscript x subscript 1 above negative 2 and a superscript y subscript 1 above 1.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_018c_img_new.jpg\" alt=\"In the third row, the first cell reads \u201cStep 3. Identify the point.\u201d The second cell reads \u201cThe given point is (negative 2, 1).\u201d The third cell contains the ordered pair (negative 2, 1) with a superscript x subscript 1 above negative 2 and a superscript y subscript 1 above 1.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169594211943\" data-type=\"media\" data-alt=\"In the fourth row, the first cell reads \u201cStep 4. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top of the second cell is blank. The third cell contains the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the form with negative 2 substituted for x subscript 1, 1 substituted for y subscript 1, and 2 substituted for m: y minus 1 equals 2 times x minus negative 2 in parentheses. One line down, the text in the second cell says \u201cSimplify.\u201d The right column contains y minus 1 equals 2 times x plus 2. Below this is y minus 1 equals 2x plus 4.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_018d_img_new.jpg\" alt=\"In the fourth row, the first cell reads \u201cStep 4. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top of the second cell is blank. The third cell contains the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the form with negative 2 substituted for x subscript 1, 1 substituted for y subscript 1, and 2 substituted for m: y minus 1 equals 2 times x minus negative 2 in parentheses. One line down, the text in the second cell says \u201cSimplify.\u201d The right column contains y minus 1 equals 2 times x plus 2. Below this is y minus 1 equals 2x plus 4.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596500464\" data-type=\"media\" data-alt=\"In the fifth row, the first cell says \u201cStep 5. Write the equation in slope-intercept form.\u201d The second cell is blank. The third cell contains y equals 2x plus 5.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_018e_img_new.jpg\" alt=\"In the fifth row, the first cell says \u201cStep 5. Write the equation in slope-intercept form.\u201d The second cell is blank. The third cell contains y equals 2x plus 5.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169594061628\">Does this equation make sense? What is the <em data-effect=\"italics\">y<\/em>-intercept of the line? What is the slope?<\/p>\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 9.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594046498\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594046502\" data-type=\"exercise\">\n<div id=\"fs-id1169594166491\" data-type=\"problem\">\n<p id=\"fs-id1169594166493\">Find an equation of a line parallel to the line \\(y=3x+1\\) that contains the point \\(\\left(4,2\\right)\\). Write the equation in slope\u2013intercept form.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596395477\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596395479\">\\(y=3x-10\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594053750\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596658472\" data-type=\"exercise\">\n<div id=\"fs-id1169596658474\" data-type=\"problem\"><\/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-id1169596658474\" data-type=\"problem\">\n<p id=\"fs-id1169596658476\">Find an equation of a line parallel to the line \\(y=\\dfrac{1}{2}x-3\\) that contains the point \\(\\left(6,4\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596232389\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596387361\">\\(y=\\dfrac{1}{2}x+1\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594053750\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596658472\" data-type=\"exercise\">\n<div id=\"fs-id1169596232389\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Find an equation of a line parallel to a given line<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169596534119\" class=\"stepwise\" type=\"1\">\n \t<li>Find the slope of the given line.<\/li>\n \t<li>Find the slope of the parallel line.<\/li>\n \t<li>Identify the point.<\/li>\n \t<li>Substitute the values into the point\u2013slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/li>\n \t<li>Write the equation in slope\u2013intercept form.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Find an Equation of a Line Perpendicular to a Given Line<\/h1>\n<p id=\"fs-id1169594051950\">Now, let\u2019s consider perpendicular lines. Suppose we need to find a line passing through a specific point and which is perpendicular to a given line. We can use the fact that perpendicular lines have slopes that are negative reciprocals. We will again use the point\u2013slope equation, like we did with parallel lines.<\/p>\n<p id=\"fs-id1169594029248\">The graph shows the graph of \\(y=2x-3\\). Now, we want to graph a line perpendicular to this line and passing through \\(\\left(-2,1\\right)\\).<\/p>\n<span id=\"fs-id1169596252399\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). Elsewhere on the graph, the point (negative 2, 1) is plotted.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_002_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). Elsewhere on the graph, the point (negative 2, 1) is plotted.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169594241368\">We know that perpendicular lines have slopes that are negative reciprocals. We\u2019ll use the notation \\({m}_{\\perp}\\) to represent the slope of a line perpendicular to a line with slope \\(m\\). (Notice that the subscript \u22a5 looks like the right angles made by two perpendicular lines.)<\/p>\n\\(\\begin{array}{ccc}\\hfill y=2x-3\\hfill &amp; &amp; \\text{perpendicular line}\\hfill \\\\ \\hfill m=2\\hfill &amp; &amp; {m}_{\\perp}=-\\dfrac{1}{2}\\hfill \\end{array}\\)\n<p id=\"fs-id1169596686478\">We now know the perpendicular line will pass through \\(\\left(-2,1\\right)\\) with \\({m}_{\\perp}=-\\dfrac{1}{2}\\).<\/p>\n<p id=\"fs-id1169596362932\">To graph the line, we will start at \\(\\left(-2,1\\right)\\) and count out the rise \\(-1\\) and the run 2. Then we draw the line.<\/p>\n<span id=\"fs-id1169596377776\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). Elsewhere, the point (negative 2, 1) is plotted. Another line perpendicular to the first line passes through the point (negative 2, 1) and intercepts the x and y-axes at (0, 0). A red line with an arrow extends left from (0, 0) to (negative 2, 0), then extends up and terminates at (negative 2, 1), forming a right triangle with the second line as a hypotenuse.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_005_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). Elsewhere, the point (negative 2, 1) is plotted. Another line perpendicular to the first line passes through the point (negative 2, 1) and intercepts the x and y-axes at (0, 0). A red line with an arrow extends left from (0, 0) to (negative 2, 0), then extends up and terminates at (negative 2, 1), forming a right triangle with the second line as a hypotenuse.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596652774\">Do the lines appear perpendicular? Does the second line pass through \\(\\left(-2,1\\right)\\)?<\/p>\n<p id=\"fs-id1169594086338\">Now, let\u2019s see how to do this algebraically. We can use either the slope\u2013intercept form or the point\u2013slope form to find an equation of a line. In this example we know one point, and can find the slope, so we will use the point\u2013slope form.<\/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 data-type=\"title\">How to Find an Equation of a Line Perpendicular to a Given Line<\/div>\n<div id=\"fs-id1169594060777\" data-type=\"exercise\">\n<div id=\"fs-id1169594060779\" data-type=\"problem\">\n<p id=\"fs-id1169594031417\">Find an equation of a line perpendicular to \\(y=2x-3\\) that contains the point \\(\\left(-2,1\\right)\\). Write the equation in slope\u2013intercept form.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596662182\" 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-id1169596648388\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Find the slope of the given line.\u201d The second cell reads: \u201cThe line is in slope-intercept form. y equals 2x minus 3.\u201d The third cell contains the slope of a line, defined as m equals 2.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_019a_img_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Find the slope of the given line.\u201d The second cell reads: \u201cThe line is in slope-intercept form. y equals 2x minus 3.\u201d The third cell contains the slope of a line, defined as m equals 2.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596404900\" data-type=\"media\" data-alt=\"In the second row, the first cell reads: \u201cStep 2. Find the slope of the perpendicular line.\u201d The second cell reads \u201cThe slopes of perpendicular lines are negative reciprocals.\u201d The third cell contains the slope of the perpendicular line, defined as m perpendicular equals negative 1 half.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_019b_img_new.jpg\" alt=\"In the second row, the first cell reads: \u201cStep 2. Find the slope of the perpendicular line.\u201d The second cell reads \u201cThe slopes of perpendicular lines are negative reciprocals.\u201d The third cell contains the slope of the perpendicular line, defined as m perpendicular equals negative 1 half.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596381059\" data-type=\"media\" data-alt=\"In the third row, the first cell reads \u201cStep 3. Identify the point.\u201d The second cell reads \u201cThe given point is (negative 2, 1).\u201d The third cell contains the ordered pair (negative 2, 1) with a superscript x subscript 1 above negative 2 and a superscript y subscript 1 above 1.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_019c_img_new.jpg\" alt=\"In the third row, the first cell reads \u201cStep 3. Identify the point.\u201d The second cell reads \u201cThe given point is (negative 2, 1).\u201d The third cell contains the ordered pair (negative 2, 1) with a superscript x subscript 1 above negative 2 and a superscript y subscript 1 above 1.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596320362\" data-type=\"media\" data-alt=\"In the fourth row, the first cell reads \u201cStep 4. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top of the second cell is blank. The third cell contains the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the form with negative 2 substituted for x subscript 1, 1 substituted for y subscript 1, and negative 1 half substituted for m: y minus 1 equals negative 1 half times x minus negative 2 in parentheses. One line down, the text in the second cell says \u201cSimplify.\u201d The right column contains y minus 1 equals negative 1 half times x plus 2. Below this is y minus 1 equals negative 1 half x plus minus 1.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_019d_img_new.jpg\" alt=\"In the fourth row, the first cell reads \u201cStep 4. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top of the second cell is blank. The third cell contains the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the form with negative 2 substituted for x subscript 1, 1 substituted for y subscript 1, and negative 1 half substituted for m: y minus 1 equals negative 1 half times x minus negative 2 in parentheses. One line down, the text in the second cell says \u201cSimplify.\u201d The right column contains y minus 1 equals negative 1 half times x plus 2. Below this is y minus 1 equals negative 1 half x plus minus 1.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596215934\" data-type=\"media\" data-alt=\"In the fifth row, the first cell says \u201cStep 5. Write the equation in slope-intercept form.\u201d The second cell is blank. The third cell contains y equals negative 1 half x.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_019e_img_new.jpg\" alt=\"In the fifth row, the first cell says \u201cStep 5. Write the equation in slope-intercept form.\u201d The second cell is blank. The third cell contains y equals negative 1 half x.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596389272\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596389275\" data-type=\"exercise\">\n<div id=\"fs-id1169594206653\" data-type=\"problem\">\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-id1169596389272\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596389275\" data-type=\"exercise\">\n<div id=\"fs-id1169594206653\" data-type=\"problem\">\n<p id=\"fs-id1169594206655\">Find an equation of a line perpendicular to the line \\(y=3x+1\\) that contains the point \\(\\left(4,2\\right)\\). Write the equation in slope\u2013intercept form.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596285437\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596285439\">\\(y=-\\dfrac{1}{3}x+\\dfrac{10}{3}\\)<\/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 10.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594060855\" data-type=\"problem\">\n<p id=\"fs-id1169594060857\">Find an equation of a line perpendicular to the line \\(y=\\dfrac{1}{2}x-3\\) that contains the point \\(\\left(6,4\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594157964\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594157966\">\\(y=-2x+16\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Find an equation of a line perpendicular to a given line<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169594031899\" class=\"stepwise\" type=\"1\">\n \t<li>Find the slope of the given line.<\/li>\n \t<li>Find the slope of the perpendicular line.<\/li>\n \t<li>Identify the point.<\/li>\n \t<li>Substitute the values into the point\u2013slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/li>\n \t<li>Write the equation in slope\u2013intercept form.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594155483\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594060852\" data-type=\"exercise\">\n<div id=\"fs-id1169594157964\" data-type=\"solution\">\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-id1169596380980\" data-type=\"problem\">\n<p id=\"fs-id1169596244473\">Find an equation of a line perpendicular to \\(x=5\\) that contains the point \\(\\left(3,-2\\right)\\). Write the equation in slope\u2013intercept form.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596555194\" 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-id1169596421863\">Again, since we know one point, the point\u2013slope option seems more promising than the slope\u2013intercept option. We need the slope to use this form, and we know the new line will be perpendicular to \\(x=5\\). This line is vertical, so its perpendicular will be horizontal. This tells us the \\({m}_{\\perp}=0\\).<\/p>\n\n<table id=\"eip-357\" class=\"unnumbered unstyled\" summary=\"\/\">\n<tbody>\n<tr>\n<td>Identify the point.<\/td>\n<td>\\(\\left(3,-2\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Identify the slope of the perpendicular line.<\/td>\n<td>\\({m}_{\\perp}=0\\)<\/td>\n<\/tr>\n<tr>\n<td>Substitute the values into \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/td>\n<td>\\(\\begin{array}{c}y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\\\ y-\\left(-2\\right)=0\\left(x-3\\right)\\\\ y+2=0\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(y=-2\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596652664\">Sketch the graph of both lines. Do they appear to be 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 11.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596534834\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596686993\" data-type=\"exercise\">\n<div id=\"fs-id1169596686995\" data-type=\"problem\">\n<p id=\"fs-id1169596686997\">Find an equation of a line that is perpendicular to the line \\(x=4\\) that contains the point \\(\\left(4,-5\\right)\\). Write the equation in slope\u2013intercept form.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596653543\" data-type=\"solution\">\n\n\\(y=-5\\)\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 11.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594079088\" data-type=\"problem\">\n<p id=\"fs-id1169594079090\">Find an equation of a line that is perpendicular to the line \\(x=2\\) that contains the point \\(\\left(2,-1\\right)\\). Write the equation in slope\u2013intercept form.<\/p>\n\n<\/div>\n<div id=\"fs-id1169594085943\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594085945\">\\(y=-1\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596320224\">In <a class=\"autogenerated-content\" href=\"#fs-id1169594157964\">(Example 11)<\/a>, we used the point\u2013slope form to find the equation. We could have looked at this in a different way.<\/p>\n<p id=\"fs-id1169596590476\">We want to find a line that is perpendicular to \\(x=5\\) that contains the point \\(\\left(3,-2\\right)\\). The graph shows us the line\\(x=5\\) and the point \\(\\left(3,-2\\right)\\).<\/p>\n<span id=\"fs-id1169596360518\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is x equals 5 intercepts the x-axis at (5, 0) and runs parallel to the y-axis. Elsewhere on the graph, the point (3, negative 2) is plotted.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_006_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is x equals 5 intercepts the x-axis at (5, 0) and runs parallel to the y-axis. Elsewhere on the graph, the point (3, negative 2) is plotted.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169594158800\">We know every line perpendicular to a vertical line is horizontal, so we will sketch the horizontal line through \\(\\left(3,-2\\right)\\).<\/p>\n<span id=\"fs-id1169594012432\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is x equals 5 intercepts the x-axis at (5, 0) and runs parallel to the y-axis. Elsewhere on the graph, the points (negative 2, negative 2), (0, negative 2), (3, negative 2), and (6, negative 2) are plotted. A line perpendicular to the previous line passes through those points and runs parallel to the x-axis.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_007_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is x equals 5 intercepts the x-axis at (5, 0) and runs parallel to the y-axis. Elsewhere on the graph, the points (negative 2, negative 2), (0, negative 2), (3, negative 2), and (6, negative 2) are plotted. A line perpendicular to the previous line passes through those points and runs parallel to the x-axis.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596438830\">Do the lines appear perpendicular?<\/p>\n<p id=\"fs-id1169596363033\">If we look at a few points on this horizontal line, we notice they all have <em data-effect=\"italics\">y<\/em>-coordinates of \\(-2\\). So, the equation of the line perpendicular to the vertical line \\(x=5\\) is \\(y=-2\\).<\/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-id1169596389098\" data-type=\"problem\">\n<p id=\"fs-id1169596389100\">Find an equation of a line that is perpendicular to \\(y=-4\\) that contains the point \\(\\left(-4,2\\right)\\).<\/p>\nWrite the equation in slope\u2013intercept form.\n\n<\/div>\n<div id=\"fs-id1169596662202\" 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-id1169596662208\">The line \\(y=-4\\) is a horizontal line. Any line perpendicular to it must be vertical, in the form \\(x=a\\). Since the perpendicular line is vertical and passes through \\(\\left(-4,2\\right)\\), every point on it has an <em data-effect=\"italics\">x<\/em>-coordinate of \\(-4\\). The equation of the perpendicular line is \\(x=-4\\). You may want to sketch the lines. Do they appear 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 12.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594176078\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1169596362956\" data-type=\"problem\">\n<p id=\"fs-id1169596362958\">Find an equation of a line that is perpendicular to the line \\(y=1\\) that contains the point \\(\\left(-5,1\\right)\\). Write the equation in slope\u2013intercept form.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596642217\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596642219\">\\(x=-5\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594001983\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594001987\" data-type=\"exercise\">\n<div id=\"fs-id1169594001990\" data-type=\"problem\"><\/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 12.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594001990\" data-type=\"problem\">\n<p id=\"fs-id1169594001992\">Find an equation of a line that is perpendicular to the line \\(y=-5\\) that contains the point \\(\\left(-4,-5\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594151456\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594151458\">\\(x=-4\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"media-2\" data-type=\"note\">\n<p id=\"fs-id1169596656043\">Access this online resource for additional instruction and practice with finding the equation of a line.<\/p>\n\n<ul id=\"fs-id1169596656047\" data-display=\"block\">\n \t<li><a href=\"https:\/\/openstax.org\/l\/25PointSlopeForm\">Use the Point-Slope 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-id1169596454747\" data-bullet-style=\"bullet\">\n \t<li><strong data-effect=\"bold\">To Find an Equation of a Line Given the Slope and a Point<\/strong>\n<ol id=\"fs-id1169596648396\" class=\"stepwise\" type=\"1\">\n \t<li>Identify the slope.<\/li>\n \t<li>Identify the point.<\/li>\n \t<li>Substitute the values into the point-slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/li>\n \t<li>Write the equation in slope-intercept form.<\/li>\n<\/ol>\n<\/li>\n \t<li><strong data-effect=\"bold\">To Find an Equation of a Line Given Two Points<\/strong>\n<ol id=\"fs-id1169594175438\" class=\"stepwise\" type=\"1\">\n \t<li>Find the slope using the given points.<\/li>\n \t<li>Choose one point.<\/li>\n \t<li>Substitute the values into the point-slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/li>\n \t<li>Write the equation in slope-intercept form.<\/li>\n<\/ol>\n<\/li>\n \t<li><strong data-effect=\"bold\">To Write and Equation of a Line<\/strong>\n<ul id=\"fs-id1169596642287\" data-bullet-style=\"open-circle\">\n \t<li>If given slope and <em data-effect=\"italics\">y<\/em>-intercept, use slope\u2013intercept form \\(y=mx+b\\).<\/li>\n \t<li>If given slope and a point, use point\u2013slope form \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/li>\n \t<li>If given two points, use point\u2013slope form \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/li>\n<\/ul>\n<\/li>\n \t<li><strong data-effect=\"bold\">To Find an Equation of a Line Parallel to a Given Line<\/strong>\n<ol id=\"fs-id1169594007902\" class=\"stepwise\" type=\"1\">\n \t<li>Find the slope of the given line.<\/li>\n \t<li>Find the slope of the parallel line.<\/li>\n \t<li>Identify the point.<\/li>\n \t<li>Substitute the values into the point-slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/li>\n \t<li>Write the equation in slope-intercept form.<\/li>\n<\/ol>\n<\/li>\n \t<li><strong data-effect=\"bold\">To Find an Equation of a Line Perpendicular to a Given Line<\/strong>\n<ol id=\"fs-id1169596656200\" class=\"stepwise\" type=\"1\">\n \t<li>Find the slope of the given line.<\/li>\n \t<li>Find the slope of the perpendicular line.<\/li>\n \t<li>Identify the point.<\/li>\n \t<li>Substitute the values into the point-slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/li>\n \t<li>Write the equation in slope-intercept form.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1 data-type=\"title\">Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1169594034186\">\n \t<dt>point\u2013slope form<\/dt>\n \t<dd id=\"fs-id1169594034192\">The point\u2013slope form of an equation of a line with slope \\(m\\) and containing the point \\(\\left({x}_{1},{y}_{1}\\right)\\) is \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\).<\/dd>\n<\/dl>\n<\/div>\n<h1 data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1169596554445\">Find an Equation of the Line Given the Slope and <em data-effect=\"italics\">y<\/em>-Intercept<\/h2>\n<p id=\"fs-id1169596446288\">In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope\u2013intercept form.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 49.9086%;\">1. slope 4 and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,1\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">2. slope 3 and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,5\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">3. slope 8 and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-6\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">4. slope 6 and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-4\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">5. slope \\(-1\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,7\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">6. slope \\(-1\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">7. slope \\(-3\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-1\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">8. slope \\(-2\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">9. slope \\(\\frac{1}{5}\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-5\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">10. slope \\(\\frac{3}{5}\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">11. slope \\(-\\frac{2}{3}\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-3\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">12. slope \\(-\\frac{3}{4}\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-2\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">13. slope 0 and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,2\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">14. slope 0 and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">15. slope \\(-4\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,0\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">16. slope \\(-3\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,0\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596653337\">In the following exercises, find the equation of the line shown in each graph. Write the equation in slope\u2013intercept form.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50.0914%;\"><span id=\"fs-id1169596253307\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, 0) is plotted. A line intercepts the y-axis at (0, 4) and intercepts the x-axis at (2, 0).\">17. <img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_202_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, 0) is plotted. A line intercepts the y-axis at (0, 4) and intercepts the x-axis at (2, 0).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.9086%;\"><span id=\"fs-id1169596653346\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (1, negative 2) is plotted. A line intercepts the y-axis at (0, negative 5), passes through the point (1, negative 2), and intercepts the x-axis at (5 thirds, 0).\">18. <img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_201_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (1, negative 2) is plotted. A line intercepts the y-axis at (0, negative 5), passes through the point (1, negative 2), and intercepts the x-axis at (5 thirds, 0).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\"><span id=\"fs-id1169596649047\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (4, 5) is plotted. A line intercepts the x-axis at (negative 8 thirds, 0), intercepts the y-axis at (0, 2), and passes through the point (4, 5).\">19. <img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_204_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (4, 5) is plotted. A line intercepts the x-axis at (negative 8 thirds, 0), intercepts the y-axis at (0, 2), and passes through the point (4, 5).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.9086%;\"><span id=\"fs-id1169596446363\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (6, 0) is plotted. A line intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (6, 0).\">20. <img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_203_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (6, 0) is plotted. A line intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (6, 0).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\"><span id=\"fs-id1169596369564\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, negative 4) is plotted. A line intercepts the x-axis at (negative 2 thirds, 0), intercepts the y-axis at (0, negative 1), and passes through the point (2, negative 4).\">21. <img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_206_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, negative 4) is plotted. A line intercepts the x-axis at (negative 2 thirds, 0), intercepts the y-axis at (0, negative 1), and passes through the point (2, negative 4).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.9086%;\"><span id=\"fs-id1169596697233\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (3, negative 1) is plotted. A line intercepts the y-axis at (0, 2), intercepts the x-axis at (9 fourths, 0), and passes through the point (3, negative 1).\">22. <img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_205_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (3, negative 1) is plotted. A line intercepts the y-axis at (0, 2), intercepts the x-axis at (9 fourths, 0), and passes through the point (3, negative 1).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\"><span id=\"fs-id1169596446489\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (negative 3, 6) is plotted. A line running parallel to the x-axis passes through (negative 3, 6) and intercepts the y-axis at (0, 6).\">23. <img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_208_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (negative 3, 6) is plotted. A line running parallel to the x-axis passes through (negative 3, 6) and intercepts the y-axis at (0, 6).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.9086%;\"><span id=\"fs-id1169596387068\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, negative 2) is plotted. A line running parallel to the x-axis intercepts the y-axis at (0, negative 2) and passes through the point (2, negative 2).\">24. <img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_207_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, negative 2) is plotted. A line running parallel to the x-axis intercepts the y-axis at (0, negative 2) and passes through the point (2, negative 2).\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596658352\">Find an Equation of the Line Given the Slope and a Point<\/h2>\n<p id=\"fs-id1169596658358\">In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope\u2013intercept form.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 49.7258%;\">25. \\(m=\\frac{3}{8}\\), point \\(\\left(8,2\\right)\\)<\/td>\n<td style=\"width: 50.2742%;\">26. \\(m=\\frac{5}{8}\\), point \\(\\left(8,3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">27. \\(m=\\frac{5}{6}\\), point \\(\\left(6,7\\right)\\)<\/td>\n<td style=\"width: 50.2742%;\">28. \\(m=\\frac{1}{6}\\), point \\(\\left(6,1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">29. \\(m=-\\frac{3}{5}\\), point \\(\\left(10,-5\\right)\\)<\/td>\n<td style=\"width: 50.2742%;\">30. \\(m=-\\frac{3}{4}\\), point \\(\\left(8,-5\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">31. \\(m=-\\frac{1}{3}\\), point \\(\\left(-9,-8\\right)\\)<\/td>\n<td style=\"width: 50.2742%;\">32. \\(m=-\\frac{1}{4}\\), point \\(\\left(-12,-6\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">33. Horizontal line containing \\(\\left(-1,4\\right)\\)<\/td>\n<td style=\"width: 50.2742%;\">34. Horizontal line containing \\(\\left(-2,5\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">35. Horizontal line containing \\(\\left(-1,-7\\right)\\)<\/td>\n<td style=\"width: 50.2742%;\">36. Horizontal line containing \\(\\left(-2,-3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">37. \\(m=-\\frac{5}{2}\\), point \\(\\left(-8,-2\\right)\\)<\/td>\n<td style=\"width: 50.2742%;\">38. \\(m=-\\frac{3}{2}\\), point \\(\\left(-4,-3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">39. \\(m=-4\\), point \\(\\left(-2,-3\\right)\\)<\/td>\n<td style=\"width: 50.2742%;\">40. \\(m=-7\\), point \\(\\left(-1,-3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">41. Horizontal line containing \\(\\left(4,-8\\right)\\)<\/td>\n<td style=\"width: 50.2742%;\">42. Horizontal line containing \\(\\left(2,-3\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169594087053\">Find an Equation of the Line Given Two Points<\/h2>\n<p id=\"fs-id1169594087059\">In the following exercises, find the equation of a line containing the given points. Write the equation in slope\u2013intercept form.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 49.9086%;\">43. \\(\\left(3,1\\right)\\) and \\(\\left(2,5\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">44. \\(\\left(2,6\\right)\\) and \\(\\left(5,3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">45. \\(\\left(2,7\\right)\\) and \\(\\left(3,8\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">46. \\(\\left(4,3\\right)\\) and \\(\\left(8,1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">47. \\(\\left(-5,-3\\right)\\) and \\(\\left(4,-6\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">48. \\(\\left(-3,-4\\right)\\) and \\(\\left(5-2\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">49. \\(\\left(-2,8\\right)\\) and \\(\\left(-4,-6\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">50. \\(\\left(-1,3\\right)\\) and \\(\\left(-6,-7\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">51. \\(\\left(3,-2\\right)\\) and \\(\\left(-4,4\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">52. \\(\\left(6,-4\\right)\\) and \\(\\left(-2,5\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">53. \\(\\left(0,-2\\right)\\) and \\(\\left(-5,-3\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">54. \\(\\left(0,4\\right)\\) and \\(\\left(2,-3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">55. \\(\\left(4,2\\right)\\) and \\(\\left(4,-3\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">56. \\(\\left(7,2\\right)\\) and \\(\\left(7,-2\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">57. \\(\\left(-2,1\\right)\\) and \\(\\left(-2,-4\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">58. \\(\\left(-7,-1\\right)\\) and \\(\\left(-7,-4\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">59. \\(\\left(6,2\\right)\\) and \\(\\left(-3,2\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">60. \\(\\left(6,1\\right)\\) and \\(\\left(0,1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">61. \\(\\left(-6,-3\\right)\\) and \\(\\left(-1,-3\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">62. \\(\\left(3,-4\\right)\\) and \\(\\left(5,-4\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">63. \\(\\left(0,0\\right)\\) and \\(\\left(1,4\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">64. \\(\\left(4,3\\right)\\) and \\(\\left(8,0\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">65. \\(\\left(-3,0\\right)\\) and \\(\\left(-7,-2\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">66. \\(\\left(-2,-3\\right)\\) and \\(\\left(-5,-6\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">67. \\(\\left(3,5\\right)\\) and \\(\\left(-7,5\\right)\\)<\/td>\n<td style=\"width: 50.0914%;\">68. \\(\\left(8,-1\\right)\\) and \\(\\left(8,-5\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169594239500\">Find an Equation of a Line Parallel to a Given Line<\/h2>\n<p id=\"fs-id1169594239506\">In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope\u2013intercept form.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 49.543%;\">69. line \\(y=3x+4\\), point \\(\\left(2,5\\right)\\)<\/td>\n<td style=\"width: 50.457%;\">70. line \\(y=4x+2\\), point \\(\\left(1,2\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.543%;\">71. line \\(y=-3x-1\\), point \\(\\left(2,-3\\right)\\)<\/td>\n<td style=\"width: 50.457%;\">72. line \\(y=-2x-3\\), point \\(\\left(-1,3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.543%;\">73. line \\(2x-y=6\\), point \\(\\left(3,0\\right)\\)<\/td>\n<td style=\"width: 50.457%;\">74. line \\(3x-y=4\\), point \\(\\left(3,1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.543%;\">75. line \\(2x+3y=6\\), point \\(\\left(0,5\\right)\\)<\/td>\n<td style=\"width: 50.457%;\">76. line \\(4x+3y=6\\), point \\(\\left(0,-3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.543%;\">77. line \\(x=-4\\), point \\(\\left(-3,-5\\right)\\)<\/td>\n<td style=\"width: 50.457%;\">78. line \\(x=-3\\), point \\(\\left(-2,-1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.543%;\">79. line \\(x-6=0\\), point \\(\\left(4,-3\\right)\\)<\/td>\n<td style=\"width: 50.457%;\">80. line \\(x-2=0\\), point \\(\\left(1,-2\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.543%;\">81. line \\(y=1\\), point \\(\\left(3,-4\\right)\\)<\/td>\n<td style=\"width: 50.457%;\">82. line \\(y=5\\), point \\(\\left(2,-2\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.543%;\">83. line \\(y+7=0\\), point \\(\\left(1,-1\\right)\\)<\/td>\n<td style=\"width: 50.457%;\">84. line \\(y+2=0\\), point \\(\\left(3,-3\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169594154482\">Find an Equation of a Line Perpendicular to a Given Line<\/h2>\n<p id=\"fs-id1169596445758\">In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope\u2013intercept form.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 112px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 51.3711%;\">85. line \\(y=-x+5\\), point \\(\\left(3,3\\right)\\)<\/td>\n<td style=\"width: 48.6289%;\">86. line \\(y=-2x+3\\), point \\(\\left(2,2\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.3711%;\">87. line \\(y=\\frac{2}{3}x-4\\), point \\(\\left(2,-4\\right)\\)<\/td>\n<td style=\"width: 48.6289%;\">88. line \\(y=\\frac{3}{4}x-2\\), point \\(\\left(-3,4\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.3711%;\">89. line \\(4x-3y=5\\), point \\(\\left(-3,2\\right)\\)<\/td>\n<td style=\"width: 48.6289%;\">90. line \\(2x-3y=8\\), point \\(\\left(4,-1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.3711%;\">91. line \\(4x+5y=-3\\), point \\(\\left(0,0\\right)\\)<\/td>\n<td style=\"width: 48.6289%;\">92. line \\(2x+5y=6\\), point \\(\\left(0,0\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.3711%;\">93. line \\(y-6=0\\), point \\(\\left(-5,-3\\right)\\)<\/td>\n<td style=\"width: 48.6289%;\">94. line \\(y-3=0\\), point \\(\\left(-2,-4\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.3711%;\">95. line <em data-effect=\"italics\">y<\/em>-axis, point \\(\\left(2,1\\right)\\)<\/td>\n<td style=\"width: 48.6289%;\">96. line <em data-effect=\"italics\">y<\/em>-axis, point \\(\\left(3,4\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Mixed Practice<\/h2>\n<p id=\"fs-id1169596662267\">In the following exercises, find the equation of each line. Write the equation in slope\u2013intercept form.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50.0914%;\">97. Containing the points \\(\\left(2,7\\right)\\) and \\(\\left(3,8\\right)\\)<\/td>\n<td style=\"width: 49.7258%;\">98. Containing the points \\(\\left(4,3\\right)\\) and \\(\\left(8,1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">99. \\(m=\\frac{5}{6}\\), containing point \\(\\left(6,7\\right)\\)<\/td>\n<td style=\"width: 49.7258%;\">100. \\(m=\\frac{1}{6}\\), containing point \\(\\left(6,1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">101. Parallel to the line \\(2x+3y=6\\), containing point \\(\\left(0,5\\right)\\)<\/td>\n<td style=\"width: 49.7258%;\">102. Parallel to the line \\(4x+3y=6\\), containing point \\(\\left(0,-3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">103. \\(m=-\\frac{3}{5}\\), containing point \\(\\left(10,-5\\right)\\)<\/td>\n<td style=\"width: 49.7258%;\">104. \\(m=-\\frac{3}{4}\\), containing point \\(\\left(8,-5\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">105. Perpendicular to the line <em data-effect=\"italics\">y<\/em>-axis, point \\(\\left(-6,2\\right)\\)<\/td>\n<td style=\"width: 49.7258%;\">106. Perpendicular to the line \\(y-1=0\\), point \\(\\left(-2,6\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">107. Containing the points \\(\\left(-2,0\\right)\\) and \\(\\left(-3,-2\\right)\\)<\/td>\n<td style=\"width: 49.7258%;\">108. Containing the points \\(\\left(4,3\\right)\\) and \\(\\left(8,1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">109. Parallel to the line \\(x=-4\\), containing point \\(\\left(-3,-5\\right)\\)<\/td>\n<td style=\"width: 49.7258%;\">110. Parallel to the line \\(x=-3\\), containing point \\(\\left(-2,-1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">111. Containing the points \\(\\left(-5,-3\\right)\\) and \\(\\left(4,-6\\right)\\)<\/td>\n<td style=\"width: 49.7258%;\">112. Containing the points \\(\\left(-3,-4\\right)\\) and \\(\\left(2,-5\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">113. Perpendicular to the line \\(4x+3y=1\\), containing point \\(\\left(0,0\\right)\\)<\/td>\n<td style=\"width: 49.7258%;\">114. Perpendicular to the line \\(x-2y=5\\), containing point \\(\\left(-2,2\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"material-set-2\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<h2 id=\"fs-id1169594008368\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 51.1883%;\">115. <strong>Fuel consumption.<\/strong> The city mpg, \\(x\\), and highway mpg, \\(y\\), of two cars are given by the points \\(\\left(29,40\\right)\\) and\\(\\left(19,28\\right)\\). Find a linear equation that models the relationship between city mpg and highway mpg.<\/td>\n<td style=\"width: 48.8117%;\">116. <strong>Cholesterol.<\/strong> The age, \\(x\\), and LDL cholesterol level, \\(y\\), of two men are given by the points \\(\\left(18,68\\right)\\) and \\(\\left(27,122\\right)\\). Find a linear equation that models the relationship between age and LDL cholesterol level.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 67.2761%;\">117. Explain in your own words why the slopes of two perpendicular lines must have opposite signs.<\/td>\n<td style=\"width: 32.724%;\">118. Why are all horizontal lines parallel?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 481px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 48.4461%;\">1. \\(y=4x+1\\)<\/td>\n<td style=\"width: 51.5539%;\">3. \\(y=8x-6\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">5. \\(y=-x+7\\)<\/td>\n<td style=\"width: 51.5539%;\">7. \\(y=-3x-1\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">9. \\(y=\\frac{1}{5}x-5\\)<\/td>\n<td style=\"width: 51.5539%;\">11. \\(y=-\\frac{2}{3}x-3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">13. \\(y=2\\)<\/td>\n<td style=\"width: 51.5539%;\">15. \\(y=-4x\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">17. \\(y=-2x+4\\)<\/td>\n<td style=\"width: 51.5539%;\">19. \\(y=\\frac{3}{4}x+2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">21. \\(y=-\\dfrac{3}{2}x-1\\)<\/td>\n<td style=\"width: 51.5539%;\">23. \\(y=6\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">25. \\(y=\\frac{3}{8}x-1\\)<\/td>\n<td style=\"width: 51.5539%;\">27. \\(y=\\frac{5}{6}x+2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">29. \\(y=-\\frac{3}{5}x+1\\)<\/td>\n<td style=\"width: 51.5539%;\">31. \\(y=-\\frac{1}{3}x-11\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">33. \\(y=4\\)<\/td>\n<td style=\"width: 51.5539%;\">35. \\(y=-7\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">37. \\(y=-\\frac{5}{2}x-22\\)<\/td>\n<td style=\"width: 51.5539%;\">39. \\(y=-4x-11\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">41. \\(y=-8\\)<\/td>\n<td style=\"width: 51.5539%;\">43. \\(y=-4x+13\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">45. \\(y=x+5\\)<\/td>\n<td style=\"width: 51.5539%;\">47. \\(y=-\\frac{1}{3}x-\\frac{14}{3}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">49. \\(y=7x+22\\)<\/td>\n<td style=\"width: 51.5539%;\">51. \\(y=-\\frac{6}{7}x+\\frac{4}{7}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">53. \\(y=\\frac{1}{5}x-2\\)<\/td>\n<td style=\"width: 51.5539%;\">55. \\(x=4\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">57. \\(x=-2\\)<\/td>\n<td style=\"width: 51.5539%;\">59. \\(y=2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">61. \\(y=-3\\)<\/td>\n<td style=\"width: 51.5539%;\">63. \\(y=4x\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">65. \\(y=\\frac{1}{2}x+\\frac{3}{2}\\)<\/td>\n<td style=\"width: 51.5539%;\">67. \\(y=5\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">69. \\(y=3x-1\\)<\/td>\n<td style=\"width: 51.5539%;\">71. \\(y=-3x+3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">73. \\(y=2x-6\\)<\/td>\n<td style=\"width: 51.5539%;\">75. \\(y=-\\frac{2}{3}x+5\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">77. \\(x=-3\\)<\/td>\n<td style=\"width: 51.5539%;\">79. \\(x=4\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">81. \\(y=-4\\)<\/td>\n<td style=\"width: 51.5539%;\">83. \\(y=-1\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">85. \\(y=x\\)<\/td>\n<td style=\"width: 51.5539%;\">87. \\(y=-\\frac{3}{2}x-1\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">89. \\(y=-\\frac{3}{4}x-\\frac{1}{4}\\)<\/td>\n<td style=\"width: 51.5539%;\">91. \\(y=\\frac{5}{4}x\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">93. \\(x=-5\\)<\/td>\n<td style=\"width: 51.5539%;\">95. \\(y=1\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">97. \\(y=x+5\\)<\/td>\n<td style=\"width: 51.5539%;\">99. \\(y=\\frac{5}{6}x+2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">101. \\(y=-\\frac{2}{3}x+5\\)<\/td>\n<td style=\"width: 51.5539%;\">103. \\(y=-\\frac{3}{5}x+1\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">105. \\(y=2\\)<\/td>\n<td style=\"width: 51.5539%;\">107. \\(y=x+2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">109. \\(x=-3\\)<\/td>\n<td style=\"width: 51.5539%;\">111. \\(y=-\\frac{1}{3}x-\\frac{14}{3}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">113. \\(y=\\frac{3}{4}x\\)<\/td>\n<td style=\"width: 51.5539%;\">115. \\(y=1.2x+5.2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">117. Answers will vary.<\/td>\n<td style=\"width: 51.5539%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cFind the 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>Find an equation of the line given 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<\/li>\n<li>Find an equation of the line given the slope and a point<\/li>\n<li>Find an equation of the line given two points<\/li>\n<li>Find an equation of a line parallel to a given line<\/li>\n<li>Find an equation of a line perpendicular to a given line<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596399867\">How do online retailers know that \u2018you may also like\u2019 a particular item based on something you just ordered? How can economists know how a rise in the minimum wage will affect the unemployment rate? How do medical researchers create drugs to target cancer cells? How can traffic engineers predict the effect on your commuting time of an increase or decrease in gas prices? It\u2019s all mathematics.<\/p>\n<p id=\"fs-id1169594212431\">You are at an exciting point in your mathematical journey as the mathematics you are studying has interesting applications in the real world.<\/p>\n<p id=\"fs-id1169596387304\">The physical sciences, social sciences, and the business world are full of situations that can be modeled with linear equations relating two variables. Data is collected and graphed. If the data points appear to form a straight line, an equation of that line can be used to predict the value of one variable based on the value of the other variable.<\/p>\n<p id=\"fs-id1169596687875\">To create a mathematical model of a linear relation between two variables, we must be able to find the equation of the line. In this section we will look at several ways to write the equation of a line. The specific method we use will be determined by what information we are given.<\/p>\n<h1>Find an Equation of the Line Given the Slope and y-Intercept<\/h1>\n<p id=\"fs-id1169596256506\">We can easily determine the slope and intercept of a line if the equation was written in slope\u2013intercept 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;\" \/>. Now, we will do the reverse\u2014we will start with the slope and <em data-effect=\"italics\">y<\/em>-intercept and use them to find the equation of the line.<\/p>\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-id1169596370489\" data-type=\"problem\">\n<p>Find an equation of a line with slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00c6d30c5f7439a21caf981437f64be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" 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-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<\/div>\n<div id=\"fs-id1169594154667\" 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-id1169596619558\">Since we are given the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line, we can substitute the needed values into the slope\u2013intercept 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;\" \/>.<\/p>\n<table id=\"eip-id1172183502249\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the top row, the instructions in the left column say \u201cName the slope.\u201d In the right column is m equals negative 7. One row down, the instructions in the left column say \u201cName the y-intercept.\u201d In the right column is the y-intercept defined as the ordered pair (0, negative 1). One row down, the instructions in the left column say \u201cSubstitute the values into y equals mx plus b.\u201d In the right column is the slope-intercept form: y equals mx plus b. Below this is the formula with negative 7 substituted for m and negative 1 substituted for b: y equals negative 7x plus negative 1. Below this is the formula simplified: y equals negative 7x minus 1.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Name the slope.<\/td>\n<td><span id=\"eip-id1172184381083\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/07\/CNX_ElemAlg_Figure_04_06_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Name the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td><span id=\"eip-id1172187819874\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute the values into <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><span id=\"eip-id1172183461192\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172177957049\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_008d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172184642450\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_008e_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 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596237406\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169596448823\">Find an equation of a line with slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4163fe34eaf19a7a1b2db44c29e26eb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" 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-e2c3a69d33f9737210f9c4f1551f4b9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596241029\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596689594\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-30f88ad91a3ae39cfc47e2ab1da1a6fc_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;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" 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 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169594011554\">Find an equation of a line with slope <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;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-017f20ea0c6fda3470cedb20ea0b5537_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596623578\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596567679\"><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;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596765935\">Sometimes, the slope and intercept need to be determined from the graph.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE\u00a0 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596395488\" data-type=\"problem\">\n<p id=\"fs-id1169596219194\">Find the equation of the line shown.<\/p>\n<p><span id=\"fs-id1169596299458\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. A line intercepts the y-axis at (0, negative 4), passes through the plotted point (3, negative 2), and intercepts the x-axis at (4, 0).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_001_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. A line intercepts the y-axis at (0, negative 4), passes through the plotted point (3, negative 2), and intercepts the x-axis at (4, 0).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id1169596539632\" 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-id1169594051395\">We need to find the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line from the graph so we can substitute the needed values into the slope\u2013intercept 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;\" \/>.<\/p>\n<p id=\"fs-id1169596273127\">To find the slope, we choose two points on the graph.<\/p>\n<p id=\"fs-id1169596311636\">The <em data-effect=\"italics\">y<\/em>-intercept is <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 the graph passes through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dbaec542907415eac32615dfae0ae911_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<table id=\"eip-id1172185967814\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the top row, the instructions in the left column say \u201cFind the slope by counting the rise and run.\u201d In the right column is m equals rise over run. Under that is m equals two thirds. One row down, the instructions in the left column say \u201cFind the y-intercept.\u201d In the right column is the y-intercept defined as the ordered pair (0, negative 4). One row down, the instructions in the left column say \u201cSubstitute the values into y equals mx plus b.\u201d In the right column is the slope-intercept form: y equals mx plus b. Below this is the formula with negative two thirds substituted for m and negative 4 substituted for b: y equals negative two thirds x minus 4.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the slope by counting the rise and run.<\/td>\n<td><span id=\"eip-id1172185623527\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187671336\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_009b_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.<\/td>\n<td><span id=\"eip-id1172187701633\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_009c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute the values into <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><span id=\"eip-id1172187191244\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_009d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172189246088\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_009e_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 id=\"fs-id1169596238261\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596387430\" data-type=\"exercise\">\n<div id=\"fs-id1169596404087\" data-type=\"problem\">\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-id1169596238261\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596387430\" data-type=\"exercise\">\n<div id=\"fs-id1169596404087\" data-type=\"problem\">\n<p id=\"fs-id1169596766107\">Find the equation of the line shown in the graph.<\/p>\n<p><span id=\"fs-id1169596701813\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. A line intercepts the x-axis at (negative 2, 0), intercepts the y-axis at (0, 1) and passes through the plotted point (5, 4).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_010_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. A line intercepts the x-axis at (negative 2, 0), intercepts the y-axis at (0, 1) and passes through the plotted point (5, 4).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id1169594053350\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596302685\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-58d2d029769d9595fa3780db0762d58d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" 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 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596402199\" data-type=\"problem\">\n<p>Find the equation of the line shown in the graph.<\/p>\n<p><span id=\"fs-id1169596396794\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. A line intercepts the y-axis at (0, negative 5), passes through the plotted point (3, negative 1), and intercepts the x-axis at (15 fourths, 0).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_011_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. A line intercepts the y-axis at (0, negative 5), passes through the plotted point (3, negative 1), and intercepts the x-axis at (15 fourths, 0).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id1169596364856\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596459716\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5fdffe21565b86f9e7623c585b58c9cc_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;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Find an Equation of the Line Given the Slope and a Point<\/h1>\n<p id=\"fs-id1169596531418\">Finding an equation of a line using the slope\u2013intercept form of the equation works well when you are given the slope and <em data-effect=\"italics\">y<\/em>-intercept or when you read them off a graph. But what happens when you have another point instead of the <em data-effect=\"italics\">y<\/em>-intercept?<\/p>\n<p id=\"fs-id1169596705156\">We are going to use the slope formula to derive another form of an equation of the line. Suppose we have a line that has 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 that contains some specific point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-daf7d3000a611d6a6b02b6093c3dfb1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#44;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -4px;\" \/> and some other point, which we will just call <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/>. We can write the slope of this line and then change it to a different form.<\/p>\n<table id=\"eip-690\" 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-38113196a3aac65e7c4e2391277bed30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#125;&#123;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"91\" style=\"vertical-align: -15px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides of the equation by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9d886976ebd76e061112bcea9fb04336_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f224eafd3a4e36be0192db2c60212d26_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;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#125;&#123;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"273\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c38081e218e515023e60c3b3ef225857_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;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#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=\"19\" width=\"174\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite the equation with the <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;\" \/> terms on the left.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eeccca68dcf93b214cf766b3ee01ff81_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;&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"175\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594212615\">This format is called the point\u2013slope form of an equation of a line.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Point\u2013slope form of an equation of a line<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596239984\">The point\u2013slope 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 containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-daf7d3000a611d6a6b02b6093c3dfb1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#44;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -4px;\" \/> is<\/p>\n<p><span id=\"fs-id1169596378255\" data-type=\"media\" data-alt=\"No alt text\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_012_img_new.jpg\" alt=\"No alt text\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596275822\">We can use the point\u2013slope form of an equation to find an equation of a line when we are given the slope and one point. Then we will rewrite the equation in slope\u2013intercept form. Most applications of linear equations use the the slope\u2013intercept form.<\/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 data-type=\"title\">Find an Equation of a Line Given the Slope and a Point<\/div>\n<div id=\"fs-id1169596405036\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169596765661\">Find an equation of a line with 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;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9bcede84590971438c1b214dc86de010_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<div id=\"fs-id1169596263363\" 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 data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Identify the slope.\u201d The text in the second cell reads: \u201cThe slope is given.\u201d The third cell contains the slope of a line, defined as m equals 2 fifths.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_016a_img_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Identify the slope.\u201d The text in the second cell reads: \u201cThe slope is given.\u201d The third cell contains the slope of a line, defined as m equals 2 fifths.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596375441\" data-type=\"media\" data-alt=\"In the second row, the first cell reads: \u201cStep 2. Identify the point.\u201d The second cell reads: \u201cThe point is given.\u201d The third cell contains the ordered pair (10, 3). A superscript x subscript 1 is written over 10, and a superscript y subscript 1 is written over 3.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_016b_img_new.jpg\" alt=\"In the second row, the first cell reads: \u201cStep 2. Identify the point.\u201d The second cell reads: \u201cThe point is given.\u201d The third cell contains the ordered pair (10, 3). A superscript x subscript 1 is written over 10, and a superscript y subscript 1 is written over 3.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596393126\" data-type=\"media\" data-alt=\"In the third row, the first cell reads: \u201cStep 3. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top line of the second cell is left blank. The third cell features the point-slope form written again: y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with 10 substituted for x subscript 1, 3 substituted for y subscript 1, and 2 fifths substituted for m: y minus 3 equals 2 fifths times x minus 10 in parentheses. One line down, the instructions in the second cell say: \u201cSimplify.\u201d In the third cell is y minus 3 equals 2 fifths x minus 4.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_016c_img_new.jpg\" alt=\"In the third row, the first cell reads: \u201cStep 3. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top line of the second cell is left blank. The third cell features the point-slope form written again: y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with 10 substituted for x subscript 1, 3 substituted for y subscript 1, and 2 fifths substituted for m: y minus 3 equals 2 fifths times x minus 10 in parentheses. One line down, the instructions in the second cell say: \u201cSimplify.\u201d In the third cell is y minus 3 equals 2 fifths x minus 4.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596308522\" data-type=\"media\" data-alt=\"In the fourth row, the first cell reads: \u201cWrite the equation in slope-intercept form.\u201d The second cell is blank. In the third cell is y equals 2 fifths x minus 1.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_016d_img_new.jpg\" alt=\"In the fourth row, the first cell reads: \u201cWrite the equation in slope-intercept form.\u201d The second cell is blank. In the third cell is y equals 2 fifths x minus 1.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596518461\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596686980\" data-type=\"exercise\">\n<div id=\"fs-id1169596522215\" data-type=\"problem\">\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-id1169596518461\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596686980\" data-type=\"exercise\">\n<div id=\"fs-id1169596522215\" data-type=\"problem\">\n<p id=\"fs-id1169596453704\">Find an equation of a line with slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1c4a55594413864b09fca93dc6a075bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"50\" style=\"vertical-align: -12px;\" \/> and containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1f1a235ff31c373d5cda1965ad172871_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596287619\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596378552\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-657e562292801fcbf7619c0663b323a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"86\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596381387\" data-type=\"exercise\">\n<div id=\"fs-id1169596238432\" data-type=\"problem\"><\/div>\n<\/div>\n<\/div>\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-id1169596238432\" data-type=\"problem\">\n<p>Find an equation of a line with 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 containing thepoint <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-71f54f04d3310c7658adb9ab7df838d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594190014\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596456617\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a13937a8951848480b0ee74323940804_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;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596381387\" data-type=\"exercise\">\n<div id=\"fs-id1169594190014\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Find an equation of a line given the slope and a point<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol class=\"stepwise\" type=\"1\">\n<li>Identify the slope.<\/li>\n<li>Identify the point.<\/li>\n<li>Substitute the values into the point-slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<li>Write the equation in slope\u2013intercept form.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"howto\" data-type=\"note\">\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 id=\"fs-id1169594030865\" data-type=\"problem\">\n<p id=\"fs-id1169596705433\">Find an equation of a line with slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-534178d0d3fffb2edec17b7c9dc333df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"64\" style=\"vertical-align: -12px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb87bfe9ba69a89c4ac12d88180c12e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<div id=\"fs-id1169596379008\" 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-id1169596421588\">Since we are given a point and the slope of the line, we can substitute the needed values into the point\u2013slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<table id=\"eip-id1172186785398\" class=\"unnumbered unstyled\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the instructions in the left column read \u201cIdentify the slope.\u201d In the right column is the slope of a line defined as m equals negative 1 third. One line down, the instructions in the left column read \u201cIdentify the point.\u201d In the right column is the ordered pair (6, negative 4), with a superscript x subscript 1 above 6 and a superscript y subscript 1 above negative 4. One line down, the instructions in the left column read: \u201cSubstitute the values into y minus y subscript 1 equals m times x minus x1 in parentheses.\u201d In the right column is the point-slope form: y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with 6 substituted for x subscript 1, negative 4 substituted for y subscript 1, and negative 1 third substituted for m: y minus negative 4 equals negative 1 third times x minus 6 in parentheses. One line down, the instructions in the left column read \u201cSimplify.\u201d In the right column is y plus 4 equals 1 third x plus 2. One line down, the instructions in the left column say \u201cWrite in slope-intercept form.\u201d In the right column is y equals negative 1 third x minus 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify the slope.<\/td>\n<td><span id=\"eip-id1172182143837\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_013a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Identify the point.<\/td>\n<td><span id=\"eip-id1172185590223\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_013b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute the values into <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><span id=\"eip-id1172189274612\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_013c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"fs-id1172187797821\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_013d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1172186829592\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_013e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write in slope\u2013intercept form.<\/td>\n<td><span id=\"eip-id1172180357508\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_013f_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 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596581490\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596554560\" data-type=\"exercise\">\n<div id=\"fs-id1169596230637\" data-type=\"problem\">\n<p id=\"fs-id1169596463601\">Find an equation of a line with 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 containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-064fbe5b13d7774ef232dcf1aebc3fa5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"61\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596375273\" data-type=\"solution\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a6f14c6d85f24d4161bce3c3303e61ff_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;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"99\" 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 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594159889\" data-type=\"problem\">\n<p id=\"fs-id1169596654471\">Find an equation of a line with slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-32641222cf31c1fb3e10dfd5bdc0680c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"64\" style=\"vertical-align: -12px;\" \/>, and containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f5437f64603e4a5ed63fa26e11681271_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596252846\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596397906\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-788ffb06bfd0d5d422c30163afa47d38_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;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"100\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594050799\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596407606\" data-type=\"exercise\">\n<div id=\"fs-id1169596252846\" data-type=\"solution\">\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-id1169596567669\" data-type=\"problem\">\n<p id=\"fs-id1169594171652\">Find an equation of a horizontal line that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aeaca1910c48ce1d63188a726ff94fc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<div id=\"fs-id1169596658323\" 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-id1169596690846\">Every horizontal line has slope 0. We can substitute the slope and points into the point\u2013slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<table id=\"eip-id1172188999774\" class=\"unnumbered unstyled\" style=\"height: 171px;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the instructions in the left column read \u201cIdentify the slope.\u201d In the right column is the slope of a line defined as m equals 0. One line down, the instructions in the left column read \u201cIdentify the point.\u201d In the right column is the ordered pair (negative 1, 2), with a superscript x subscript 1 above negative 1 and a superscript y subscript 1 above 2. One line down, the instructions in the left column read: \u201cSubstitute the values into y minus y subscript 1 equals m times x minus x1 in parentheses.\u201d In the right column is the point-slope form: y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with negative 1 substituted for x subscript 1, 2 substituted for y subscript 1, and 0 substituted for m: y minus 2 equals 0 times x minus negative 1 in parentheses. One line down, the instructions in the left column read \u201cSimplify.\u201d In the right column is y minus 2 equals 0 times x plus 1 in parentheses. Below this is y minus 2 equals 0. Below this is y equals 2. One line down, the instructions in the left column say \u201cWrite in slope-intercept form.\u201d In the right column is the sentence: \u201cIt is in y-form, but could be written y equals 0x plus 2.\u201d\" data-label=\"\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 394.406px;\">Identify the slope.<\/td>\n<td style=\"height: 15px; width: 286.406px;\"><span id=\"fs-id1172188100755\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_014a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 39px;\">\n<td style=\"height: 39px; width: 394.406px;\">Identify the point.<\/td>\n<td style=\"height: 39px; width: 286.406px;\"><span id=\"eip-id1172189048714\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_014b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 394.406px;\">Substitute the values into <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td style=\"height: 19px; width: 286.406px;\"><span id=\"eip-id1172187183087\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_014c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 394.406px;\"><\/td>\n<td style=\"height: 22px; width: 286.406px;\"><span id=\"eip-id1172189038480\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_014d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 394.406px;\">Simplify.<\/td>\n<td style=\"height: 22px; width: 286.406px;\"><span id=\"eip-id1172187655483\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_014e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 394.406px;\"><\/td>\n<td style=\"height: 19px; width: 286.406px;\"><span id=\"eip-id1172179992212\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_014f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 21px;\">\n<td style=\"height: 21px; width: 394.406px;\"><\/td>\n<td style=\"height: 21px; width: 286.406px;\"><span id=\"eip-id1172187710403\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_014g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 394.406px;\">Write in slope\u2013intercept form.<\/td>\n<td style=\"height: 14px; width: 286.406px;\">It is in <em data-effect=\"italics\">y<\/em>-form, but could be written <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-32af798cd7480e32130bcab9e9d0801c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596244548\">Did we end up with the form of a horizontal line, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e251a16683f92cd7bf4ae744f6910d3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: -4px;\" \/>?<\/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 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596237823\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596497043\" data-type=\"exercise\">\n<div id=\"fs-id1169596302137\" data-type=\"problem\">\n<p id=\"fs-id1169594011646\">Find an equation of a horizontal line containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a59cae04d66c511c3609b538987ab5c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596441972\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596404583\"><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;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\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 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596311838\" data-type=\"problem\">\n<p id=\"fs-id1169596641169\">Find an equation of a horizontal line containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b098ad691d3b1e66796376e6000e2385_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596236922\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594001376\"><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;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Find an Equation of the Line Given Two Points<\/h1>\n<p id=\"fs-id1169596382559\">When real-world data is collected, a linear model can be created from two data points. In the next example we\u2019ll see how to find an equation of a line when just two points are given.<\/p>\n<p id=\"fs-id1169594031514\">We have two options so far for finding an equation of a line: slope\u2013intercept or point\u2013slope. Since we will know two points, it will make more sense to use the point\u2013slope form.<\/p>\n<p id=\"fs-id1169594171676\">But then we need the slope. Can we find the slope with just two points? Yes. Then, once we have the slope, we can use it and one of the given points to find the equation.<\/p>\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 data-type=\"title\">Find an Equation of a Line Given Two Points<\/div>\n<div id=\"fs-id1169596404489\" data-type=\"exercise\">\n<div id=\"fs-id1169596403384\" data-type=\"problem\">\n<p id=\"fs-id1169596685051\">Find an equation of a line that contains the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f721d5513f52f88fbefa5f38e5679ddc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#52;&#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-d1fa2be7ed8e95fd6a934ca178fab1d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<div id=\"fs-id1169594171993\" 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-id1169596765807\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Find the slope using the given points.\u201d The text in the second cell reads: \u201cTo use the point-slope form, we first find the slope.\u201d The third cell contains the slope of a line formula: m equals y superscript 2 minus y superscript 1 divided by x superscript 2 minus x superscript 1. Below this is m equals 6 minus 4 divided by 3 minus 5. Below this is m equals 2 divided by negative 2. Below this is m equals negative 1.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_017a_img_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Find the slope using the given points.\u201d The text in the second cell reads: \u201cTo use the point-slope form, we first find the slope.\u201d The third cell contains the slope of a line formula: m equals y superscript 2 minus y superscript 1 divided by x superscript 2 minus x superscript 1. Below this is m equals 6 minus 4 divided by 3 minus 5. Below this is m equals 2 divided by negative 2. Below this is m equals negative 1.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169594096777\" data-type=\"media\" data-alt=\"In the second row, the first cell reads: \u201cStep 2. Choose one point.\u201d The second cell reads: \u201cChoose either point.\u201d The third cell contains the ordered pair (5, 4) with a superscript x subscript 1 over 5 and a superscript y subscript 1 over 4.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_017b_img_new.jpg\" alt=\"In the second row, the first cell reads: \u201cStep 2. Choose one point.\u201d The second cell reads: \u201cChoose either point.\u201d The third cell contains the ordered pair (5, 4) with a superscript x subscript 1 over 5 and a superscript y subscript 1 over 4.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596705616\" data-type=\"media\" data-alt=\"In the third row, the first cell reads: \u201cStep 3. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top line of the second cell is left blank. The third cell contains the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with 5 substituted for x subscript 1, 4 substituted for y subscript 1, and negative 1 substituted for m: y minus 4 equals negative 1 times x minus 5 in parentheses. Below this is y minus 4 equals negative x plus 5.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_017c_img_new.jpg\" alt=\"In the third row, the first cell reads: \u201cStep 3. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top line of the second cell is left blank. The third cell contains the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with 5 substituted for x subscript 1, 4 substituted for y subscript 1, and negative 1 substituted for m: y minus 4 equals negative 1 times x minus 5 in parentheses. Below this is y minus 4 equals negative x plus 5.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596641032\" data-type=\"media\" data-alt=\"In the fourth row, the first cell reads: \u201cStep 4. Write the equation in slope-intercept form.\u201d The second cell is blank. The third cell contains y equals negative x plus 9.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_017d_img_new.jpg\" alt=\"In the fourth row, the first cell reads: \u201cStep 4. Write the equation in slope-intercept form.\u201d The second cell is blank. The third cell contains y equals negative x plus 9.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596701610\">Use the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d1fa2be7ed8e95fd6a934ca178fab1d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> and see that you get the same equation.<\/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 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596226961\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596368188\" data-type=\"exercise\">\n<div id=\"fs-id1169596439932\" data-type=\"problem\">\n<p id=\"fs-id1169596439934\">Find an equation of a line containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4307e3633578c7e56f8f767895b20497_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#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-097e6e0448858f11457fcdbfe715f6fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596262261\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596262263\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ff663867630c1551d9c9fa6acc22b172_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;&#120;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#51;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"97\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594157526\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594157529\" data-type=\"exercise\">\n<div id=\"fs-id1169594054336\" data-type=\"problem\"><\/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 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594054336\" data-type=\"problem\">\n<p id=\"fs-id1169594054339\">Find an equation of a line containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3ab73a57c5e039ffb22ed1a8e29747bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#52;&#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-ccc35b92a6567ced556cb46473589564_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596435824\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596435826\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e5a0fa13cc0ed42c704f6a3d2df4fd0f_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;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"111\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594157526\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594157529\" data-type=\"exercise\">\n<div id=\"fs-id1169596435824\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Find an equation of a line given two points<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169596765707\" class=\"stepwise\" type=\"1\">\n<li>Find the slope using the given points.<\/li>\n<li>Choose one point.<\/li>\n<li>Substitute the values into the point-slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<li>Write the equation in slope\u2013intercept form.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596655632\" class=\"howto\" data-type=\"note\">\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-id1169596650155\" data-type=\"problem\">\n<p id=\"fs-id1169596399264\">Find an equation of a line that contains the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d29d505cec09336aa569e1cca8670699_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8fbb5d034d8bc7481119846ba5facddb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<div id=\"fs-id1169596399218\" 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-id1169594159208\">Since we have two points, we will find an equation of the line using the point\u2013slope form. The first step will be to find the slope.<\/p>\n<table id=\"eip-id1172185786628\" class=\"unnumbered unstyled\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the instructions in the left column say \u201cFind the slope of the line through (negative 3, negative 1) and (2, negative 2).\u201d The right column contains the slope of a line formula: m equals y superscript 2 minus y superscript 1 divided by x superscript 2 minus x superscript 1. Below this is m equals negative 2 minus negative 1 divided by 2 minus negative 3. Below this is m equals negative 1 divided by 5. Below this is m equals negative 1 fifth. One line down, the instructions on the left say \u201cChoose either point.\u201d In the right column is the ordered pair (2, negative 2) with a superscript x subscript 1 over the 2 and a superscript y subscript 1 over the negative 2. One line down, the instructions on the left say \u201cSubstitute the values into y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d In the right column is the point-slope form: y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with 2 substituted for x subscript 1, negative 2 substituted for y subscript 1, and negative 1 fifth for m: y minus negative 2 equals negative 1 fifth times x minus 2 in parentheses. Below this is y plus 2 equals negative 1 fifth x plus 2 fifths. One line down, the instructions in the left column say \u201cWrite in slope-intercept form.\u201d In the right column is y equals negative 1 fifth x minus 8 fifths.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the slope of the line through (\u22123, \u22121) and (2, \u22122).<\/td>\n<td><span id=\"eip-id1172185615472\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182398829\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172189398997\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187401152\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Choose either point.<\/td>\n<td><span id=\"eip-id1172186829636\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute the values into <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><span id=\"eip-id1172187700633\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187671402\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182554715\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write in slope\u2013intercept form.<\/td>\n<td><span id=\"eip-id1172187692226\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_015i_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-id1169596244226\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596244230\" data-type=\"exercise\">\n<div id=\"fs-id1169596767375\" data-type=\"problem\">\n<p id=\"fs-id1169596767378\">Find an equation of a line containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ecc91b8d5e91ea23c08fcf2ee52342c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-876cb3caf33e984a34d443f2b79f105e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596231371\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596231373\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-afe18a6b0c38db759a5500edd1352bdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#120;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"97\" 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 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594002070\" data-type=\"problem\">\n<p id=\"fs-id1169596691700\">Find an equation of a line containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ebe785a1a1f173c2cb47dc17a15cdc63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-91e09d029e9b798ea0b0617171c88cca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594084438\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596389137\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b158ec3d4a72729316296b4eda93a5e0_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;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"111\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594002067\" data-type=\"exercise\">\n<div id=\"fs-id1169594084438\" data-type=\"solution\">\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 data-type=\"problem\">\n<p id=\"fs-id1169596621548\">Find an equation of a line that contains the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ab12b849de44ae6a90ccee83f8e1018_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e6b25c6279fe53efe7c78796a156eeed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<div id=\"fs-id1169594031440\" 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-id1169594031442\">Again, the first step will be to find the slope.<\/p>\n<table id=\"eip-312\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Find the slope of the line through (-2,4) and (-2,-3).<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b3f73755cfea11ad6340a9ab624a8629_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#95;&#123;&#50;&#125;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#125;&#123;&#123;&#120;&#125;&#95;&#123;&#50;&#125;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"99\" style=\"vertical-align: -15px;\" \/><\/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-4e1aa0b6c849bf3ff8f0a268331a123a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#51;&#45;&#52;&#125;&#123;&#45;&#50;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"122\" style=\"vertical-align: -17px;\" \/><\/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-33c404b6e892c17d1867a39062772955_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#45;&#55;&#125;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"64\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>The slope is undefined.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594178108\">This tells us it is a vertical line. Both of our points have an <em data-effect=\"italics\">x<\/em>-coordinate of <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;\" \/>. So our equation of the line is <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;\" \/>. 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;\" \/>, we cannot write it in slope\u2013intercept form.<\/p>\n<p id=\"fs-id1169594049404\">You may want to sketch a graph using the two given points. Does the graph agree with our conclusion that this is a vertical 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 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596586954\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596588167\" data-type=\"exercise\">\n<div id=\"fs-id1169596588169\" data-type=\"problem\">\n<p id=\"fs-id1169596766626\">Find an equation of a line containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b932df7404bba7c4812c40fc6d0d4b4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#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-12aeb9559a0d3673fa3759c68e52b96b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596437422\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596369550\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594041658\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594041661\" data-type=\"exercise\">\n<div id=\"fs-id1169594243909\" data-type=\"problem\"><\/div>\n<\/div>\n<\/div>\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 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594243909\" data-type=\"problem\">\n<p id=\"fs-id1169594243911\">Find an equation of a line containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6bd03bb09a34e49dd9f3ebf548e3dab1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4d4c06de3c48d63deaeaa1d43ed2ba09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596252026\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596252028\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b3dc975a98ccada6f136856736d7df06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596500442\">We have seen that we can use either the slope\u2013intercept form or the point\u2013slope form to find an equation of a line. Which form we use will depend on the information we are given. This is summarized in the following table.<\/p>\n<table id=\"fs-id1169596518320\" class=\"aligncenter\" summary=\"The top row of this table is a header row, which names the table: \u201cTo Write an Equation of a Line\u201d. The second row, which is also a header row, is split into three cells, and each cell names the column below it. From left to right, the first column is \u201cIf given,\u201d the second column is \u201cUse\u201d, and the third column is \u201cForm\u201d. In the third row, the \u201cIf given\u201d column contains \u2018Slope and y-intercept\u201d, the \u201cUse\u201d column contains \u201cslope-intercept\u201d, and the \u201cForm\u201d column contains the formula y equals mx plus b. In the fourth row, the \u201cIf given\u201d column contains \u201cSlope and a point\u201d, the \u201cUse\u201d column contains \u201cpoint-slope\u201d, and the \u201cForm\u201d column contains the formula y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. In the fifth row, the \u201cIf given\u201d column contains \u201cTwo points\u201d, the \u201cUse\u201d column contains \u201cpoint-slope\u201d, and the third column contains the same formula as before: y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\">\n<caption>To Write an Equation of a Line<\/caption>\n<tbody>\n<tr>\n<th scope=\"col\" data-valign=\"middle\" data-align=\"left\">If given:<\/th>\n<th scope=\"col\" data-valign=\"middle\" data-align=\"left\">Use:<\/th>\n<th scope=\"col\" data-valign=\"middle\" data-align=\"left\">Form:<\/th>\n<\/tr>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Slope and <em data-effect=\"italics\">y<\/em>-intercept<\/td>\n<td data-valign=\"middle\" data-align=\"left\">slope\u2013intercept<\/td>\n<td data-valign=\"middle\" data-align=\"left\"><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 data-valign=\"middle\" data-align=\"left\">Slope and a point<\/td>\n<td data-valign=\"middle\" data-align=\"left\">point\u2013slope<\/td>\n<td data-valign=\"middle\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Two points<\/td>\n<td data-valign=\"middle\" data-align=\"left\">point\u2013slope<\/td>\n<td data-valign=\"middle\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1 data-type=\"title\">Find an Equation of a Line Parallel to a Given Line<\/h1>\n<p id=\"fs-id1169596373155\">Suppose we need to find an equation of a line that passes through a specific point and is parallel to a given line. We can use the fact that parallel lines have the same slope. So we will have a point and the slope\u2014just what we need to use the point\u2013slope equation.<\/p>\n<p id=\"fs-id1169594097298\">First let\u2019s look at this graphically.<\/p>\n<p id=\"fs-id1169596361007\">The graph shows the graph of <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;\" \/>. We want to graph a line parallel to this line and passing through the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><span id=\"fs-id1169596656632\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). Elsewhere on the graph, the point (negative 2, 1) is plotted.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_002_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). Elsewhere on the graph, the point (negative 2, 1) is plotted.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596377643\">We know that parallel lines have the same slope. So the second line will have the same slope as<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;\" \/>. That slope is<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1d8b8fd6d9f4f70b3fe74e3bbd11c24d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#92;&#112;&#97;&#114;&#97;&#108;&#108;&#101;&#108;&#32;&#125;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"55\" style=\"vertical-align: -8px;\" \/>. We\u2019ll use the notation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-317be5f65ae274c1a6831a4dd467bc71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#92;&#112;&#97;&#114;&#97;&#108;&#108;&#101;&#108;&#32;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"22\" style=\"vertical-align: -8px;\" \/> to represent the slope of a line parallel to 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;\" \/>. (Notice that the subscript <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d69b7dbc5946cec382ffda642400dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#97;&#114;&#97;&#108;&#108;&#101;&#108;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"5\" style=\"vertical-align: -5px;\" \/> looks like two parallel lines.)<\/p>\n<p id=\"fs-id1169594052366\">The second line will pass through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and have <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ee3bb14bbe97a1114d697f8b45a9f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/>. To graph the line, we start at<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and count out the rise and run. With <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ee3bb14bbe97a1114d697f8b45a9f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/> (or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23b08319261909c2e8fe49d2d1ccb8c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"50\" style=\"vertical-align: -12px;\" \/>), we count out the rise 2 and the run 1. We draw the line.<\/p>\n<p><span id=\"fs-id1169596288671\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). The points (negative 2, 1) and (negative 1, 3) are plotted. A second line, parallel to the first, intercepts the x-axis at (negative 5 halves, 0), passes through the points (negative 2, 1) and (negative 1, 3), and intercepts the y-axis at (0, 5).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_003_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). The points (negative 2, 1) and (negative 1, 3) are plotted. A second line, parallel to the first, intercepts the x-axis at (negative 5 halves, 0), passes through the points (negative 2, 1) and (negative 1, 3), and intercepts the y-axis at (0, 5).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169594053849\">Do the lines appear parallel? Does the second line pass through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>?<\/p>\n<p id=\"fs-id1169594166872\">Now, let\u2019s see how to do this algebraically.<\/p>\n<p id=\"fs-id1169594166876\">We can use either the slope\u2013intercept form or the point\u2013slope form to find an equation of a line. Here we know one point and can find the slope. So we will use the point\u2013slope form.<\/p>\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 data-type=\"title\">How to Find an Equation of a Line Parallel to a Given Line<\/div>\n<div id=\"fs-id1169596468343\" data-type=\"exercise\">\n<div id=\"fs-id1169596468345\" data-type=\"problem\">\n<p id=\"fs-id1169596361101\">Find an equation of a line parallel to <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;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<div id=\"fs-id1169596662604\" 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-id1169596514414\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Find the slope of the given line.\u201d The second cell reads: \u201cThe line is in slope-intercept form. y equals 2x minus 3.\u201d The third cell contains the slope of a line, defined as m equals 2.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_018a_img_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Find the slope of the given line.\u201d The second cell reads: \u201cThe line is in slope-intercept form. y equals 2x minus 3.\u201d The third cell contains the slope of a line, defined as m equals 2.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169594087301\" data-type=\"media\" data-alt=\"In the second row, the first cell reads: \u201cStep 2. Find the slope of the parallel line.\u201d The second cell reads \u201cParallel lines have the same slope.\u201d The third cell contains the slope of the parallel line, defined as m parallel equals 2.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_018b_img_new.jpg\" alt=\"In the second row, the first cell reads: \u201cStep 2. Find the slope of the parallel line.\u201d The second cell reads \u201cParallel lines have the same slope.\u201d The third cell contains the slope of the parallel line, defined as m parallel equals 2.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596634681\" data-type=\"media\" data-alt=\"In the third row, the first cell reads \u201cStep 3. Identify the point.\u201d The second cell reads \u201cThe given point is (negative 2, 1).\u201d The third cell contains the ordered pair (negative 2, 1) with a superscript x subscript 1 above negative 2 and a superscript y subscript 1 above 1.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_018c_img_new.jpg\" alt=\"In the third row, the first cell reads \u201cStep 3. Identify the point.\u201d The second cell reads \u201cThe given point is (negative 2, 1).\u201d The third cell contains the ordered pair (negative 2, 1) with a superscript x subscript 1 above negative 2 and a superscript y subscript 1 above 1.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169594211943\" data-type=\"media\" data-alt=\"In the fourth row, the first cell reads \u201cStep 4. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top of the second cell is blank. The third cell contains the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the form with negative 2 substituted for x subscript 1, 1 substituted for y subscript 1, and 2 substituted for m: y minus 1 equals 2 times x minus negative 2 in parentheses. One line down, the text in the second cell says \u201cSimplify.\u201d The right column contains y minus 1 equals 2 times x plus 2. Below this is y minus 1 equals 2x plus 4.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_018d_img_new.jpg\" alt=\"In the fourth row, the first cell reads \u201cStep 4. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top of the second cell is blank. The third cell contains the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the form with negative 2 substituted for x subscript 1, 1 substituted for y subscript 1, and 2 substituted for m: y minus 1 equals 2 times x minus negative 2 in parentheses. One line down, the text in the second cell says \u201cSimplify.\u201d The right column contains y minus 1 equals 2 times x plus 2. Below this is y minus 1 equals 2x plus 4.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596500464\" data-type=\"media\" data-alt=\"In the fifth row, the first cell says \u201cStep 5. Write the equation in slope-intercept form.\u201d The second cell is blank. The third cell contains y equals 2x plus 5.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_018e_img_new.jpg\" alt=\"In the fifth row, the first cell says \u201cStep 5. Write the equation in slope-intercept form.\u201d The second cell is blank. The third cell contains y equals 2x plus 5.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169594061628\">Does this equation make sense? What is the <em data-effect=\"italics\">y<\/em>-intercept of the line? What is the slope?<\/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 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594046498\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594046502\" data-type=\"exercise\">\n<div id=\"fs-id1169594166491\" data-type=\"problem\">\n<p id=\"fs-id1169594166493\">Find an equation of a line parallel to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-15253001234eb31db5eff50664eacd78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb6560ec04491f4e7cf02e14e6df5ec3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<div id=\"fs-id1169596395477\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596395479\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-664b8b828b69575feb482f8daae0f302_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594053750\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596658472\" data-type=\"exercise\">\n<div id=\"fs-id1169596658474\" data-type=\"problem\"><\/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-id1169596658474\" data-type=\"problem\">\n<p id=\"fs-id1169596658476\">Find an equation of a line parallel to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-509a3d8cc857334ee3b11b9b6b164a09_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;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-86825c0bacfa777b8fe368820523b723_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596232389\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596387361\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-77690636b5da08b83798c9f513d2de0c_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;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594053750\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596658472\" data-type=\"exercise\">\n<div id=\"fs-id1169596232389\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Find an equation of a line parallel to a given line<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169596534119\" class=\"stepwise\" type=\"1\">\n<li>Find the slope of the given line.<\/li>\n<li>Find the slope of the parallel line.<\/li>\n<li>Identify the point.<\/li>\n<li>Substitute the values into the point\u2013slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<li>Write the equation in slope\u2013intercept form.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Find an Equation of a Line Perpendicular to a Given Line<\/h1>\n<p id=\"fs-id1169594051950\">Now, let\u2019s consider perpendicular lines. Suppose we need to find a line passing through a specific point and which is perpendicular to a given line. We can use the fact that perpendicular lines have slopes that are negative reciprocals. We will again use the point\u2013slope equation, like we did with parallel lines.<\/p>\n<p id=\"fs-id1169594029248\">The graph shows the graph of <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;\" \/>. Now, we want to graph a line perpendicular to this line and passing through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><span id=\"fs-id1169596252399\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). Elsewhere on the graph, the point (negative 2, 1) is plotted.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_002_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). Elsewhere on the graph, the point (negative 2, 1) is plotted.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169594241368\">We know that perpendicular lines have slopes that are negative reciprocals. We\u2019ll use the notation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-53406ca82f970fcc2160a8754a8f838b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#92;&#112;&#101;&#114;&#112;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"26\" style=\"vertical-align: -3px;\" \/> to represent the slope of a line perpendicular to 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;\" \/>. (Notice that the subscript \u22a5 looks like the right angles made by two perpendicular lines.)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00c5ac0db9b4ad2fe234af2ed306e652_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;&#121;&#61;&#50;&#120;&#45;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#101;&#114;&#112;&#101;&#110;&#100;&#105;&#99;&#117;&#108;&#97;&#114;&#32;&#108;&#105;&#110;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#109;&#61;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#123;&#109;&#125;&#95;&#123;&#92;&#112;&#101;&#114;&#112;&#125;&#61;&#45;&#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=\"54\" width=\"255\" style=\"vertical-align: -24px;\" \/><\/p>\n<p id=\"fs-id1169596686478\">We now know the perpendicular line will pass through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2c91094e7183baf6ecfc4aa1e6360ee0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#92;&#112;&#101;&#114;&#112;&#125;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"75\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<p id=\"fs-id1169596362932\">To graph the line, we will start at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and count out the rise <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;\" \/> and the run 2. Then we draw the line.<\/p>\n<p><span id=\"fs-id1169596377776\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). Elsewhere, the point (negative 2, 1) is plotted. Another line perpendicular to the first line passes through the point (negative 2, 1) and intercepts the x and y-axes at (0, 0). A red line with an arrow extends left from (0, 0) to (negative 2, 0), then extends up and terminates at (negative 2, 1), forming a right triangle with the second line as a hypotenuse.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_005_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). Elsewhere, the point (negative 2, 1) is plotted. Another line perpendicular to the first line passes through the point (negative 2, 1) and intercepts the x and y-axes at (0, 0). A red line with an arrow extends left from (0, 0) to (negative 2, 0), then extends up and terminates at (negative 2, 1), forming a right triangle with the second line as a hypotenuse.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596652774\">Do the lines appear perpendicular? Does the second line pass through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>?<\/p>\n<p id=\"fs-id1169594086338\">Now, let\u2019s see how to do this algebraically. We can use either the slope\u2013intercept form or the point\u2013slope form to find an equation of a line. In this example we know one point, and can find the slope, so we will use the point\u2013slope form.<\/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 data-type=\"title\">How to Find an Equation of a Line Perpendicular to a Given Line<\/div>\n<div id=\"fs-id1169594060777\" data-type=\"exercise\">\n<div id=\"fs-id1169594060779\" data-type=\"problem\">\n<p id=\"fs-id1169594031417\">Find an equation of a line perpendicular to <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;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<div id=\"fs-id1169596662182\" 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-id1169596648388\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Find the slope of the given line.\u201d The second cell reads: \u201cThe line is in slope-intercept form. y equals 2x minus 3.\u201d The third cell contains the slope of a line, defined as m equals 2.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_019a_img_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: \u201cStep 1. Find the slope of the given line.\u201d The second cell reads: \u201cThe line is in slope-intercept form. y equals 2x minus 3.\u201d The third cell contains the slope of a line, defined as m equals 2.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596404900\" data-type=\"media\" data-alt=\"In the second row, the first cell reads: \u201cStep 2. Find the slope of the perpendicular line.\u201d The second cell reads \u201cThe slopes of perpendicular lines are negative reciprocals.\u201d The third cell contains the slope of the perpendicular line, defined as m perpendicular equals negative 1 half.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_019b_img_new.jpg\" alt=\"In the second row, the first cell reads: \u201cStep 2. Find the slope of the perpendicular line.\u201d The second cell reads \u201cThe slopes of perpendicular lines are negative reciprocals.\u201d The third cell contains the slope of the perpendicular line, defined as m perpendicular equals negative 1 half.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596381059\" data-type=\"media\" data-alt=\"In the third row, the first cell reads \u201cStep 3. Identify the point.\u201d The second cell reads \u201cThe given point is (negative 2, 1).\u201d The third cell contains the ordered pair (negative 2, 1) with a superscript x subscript 1 above negative 2 and a superscript y subscript 1 above 1.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_019c_img_new.jpg\" alt=\"In the third row, the first cell reads \u201cStep 3. Identify the point.\u201d The second cell reads \u201cThe given point is (negative 2, 1).\u201d The third cell contains the ordered pair (negative 2, 1) with a superscript x subscript 1 above negative 2 and a superscript y subscript 1 above 1.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596320362\" data-type=\"media\" data-alt=\"In the fourth row, the first cell reads \u201cStep 4. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top of the second cell is blank. The third cell contains the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the form with negative 2 substituted for x subscript 1, 1 substituted for y subscript 1, and negative 1 half substituted for m: y minus 1 equals negative 1 half times x minus negative 2 in parentheses. One line down, the text in the second cell says \u201cSimplify.\u201d The right column contains y minus 1 equals negative 1 half times x plus 2. Below this is y minus 1 equals negative 1 half x plus minus 1.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_019d_img_new.jpg\" alt=\"In the fourth row, the first cell reads \u201cStep 4. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.\u201d The top of the second cell is blank. The third cell contains the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the form with negative 2 substituted for x subscript 1, 1 substituted for y subscript 1, and negative 1 half substituted for m: y minus 1 equals negative 1 half times x minus negative 2 in parentheses. One line down, the text in the second cell says \u201cSimplify.\u201d The right column contains y minus 1 equals negative 1 half times x plus 2. Below this is y minus 1 equals negative 1 half x plus minus 1.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596215934\" data-type=\"media\" data-alt=\"In the fifth row, the first cell says \u201cStep 5. Write the equation in slope-intercept form.\u201d The second cell is blank. The third cell contains y equals negative 1 half x.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_019e_img_new.jpg\" alt=\"In the fifth row, the first cell says \u201cStep 5. Write the equation in slope-intercept form.\u201d The second cell is blank. The third cell contains y equals negative 1 half x.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596389272\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596389275\" data-type=\"exercise\">\n<div id=\"fs-id1169594206653\" data-type=\"problem\">\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-id1169596389272\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596389275\" data-type=\"exercise\">\n<div id=\"fs-id1169594206653\" data-type=\"problem\">\n<p id=\"fs-id1169594206655\">Find an equation of a line perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-15253001234eb31db5eff50664eacd78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb6560ec04491f4e7cf02e14e6df5ec3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<div id=\"fs-id1169596285437\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596285439\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-73d97bd46db40c8eeb715a147bf1a947_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;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"111\" 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 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594060855\" data-type=\"problem\">\n<p id=\"fs-id1169594060857\">Find an equation of a line perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-509a3d8cc857334ee3b11b9b6b164a09_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;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-86825c0bacfa777b8fe368820523b723_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594157964\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594157966\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a4fbd762ab5dc494da02f8e86c299946_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;&#120;&#43;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"105\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Find an equation of a line perpendicular to a given line<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169594031899\" class=\"stepwise\" type=\"1\">\n<li>Find the slope of the given line.<\/li>\n<li>Find the slope of the perpendicular line.<\/li>\n<li>Identify the point.<\/li>\n<li>Substitute the values into the point\u2013slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<li>Write the equation in slope\u2013intercept form.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594155483\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594060852\" data-type=\"exercise\">\n<div id=\"fs-id1169594157964\" data-type=\"solution\">\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-id1169596380980\" data-type=\"problem\">\n<p id=\"fs-id1169596244473\">Find an equation of a line perpendicular to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dbaec542907415eac32615dfae0ae911_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<div id=\"fs-id1169596555194\" 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-id1169596421863\">Again, since we know one point, the point\u2013slope option seems more promising than the slope\u2013intercept option. We need the slope to use this form, and we know the new line will be perpendicular to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/>. This line is vertical, so its perpendicular will be horizontal. This tells us the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-be8d741efded967e03514b8e86eea417_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#92;&#112;&#101;&#114;&#112;&#125;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: -3px;\" \/>.<\/p>\n<table id=\"eip-357\" class=\"unnumbered unstyled\" summary=\"\/\">\n<tbody>\n<tr>\n<td>Identify the point.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dbaec542907415eac32615dfae0ae911_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#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<\/tr>\n<tr>\n<td>Identify the slope of the perpendicular line.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-be8d741efded967e03514b8e86eea417_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#92;&#112;&#101;&#114;&#112;&#125;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: -3px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Substitute the values into <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cfc6718b4b82e54ef44de60a337fd11c_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;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#121;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#121;&#43;&#50;&#61;&#48;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"157\" style=\"vertical-align: -26px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f986dbfac9d3f29a18cba91e9efa9d2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596652664\">Sketch the graph of both lines. Do they appear to be 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 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596534834\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596686993\" data-type=\"exercise\">\n<div id=\"fs-id1169596686995\" data-type=\"problem\">\n<p id=\"fs-id1169596686997\">Find an equation of a line that is perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2145acc2878ed61214887e120f2485b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: -1px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-29aa507469690430f5f6a9749db9f962_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596653543\" data-type=\"solution\">\n<p><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;\" \/><\/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 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594079088\" data-type=\"problem\">\n<p id=\"fs-id1169594079090\">Find an equation of a line that is perpendicular to the line <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;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-25c4864d7eaa7ae5b2fe81ae29cf46af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<div id=\"fs-id1169594085943\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594085945\"><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;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596320224\">In <a class=\"autogenerated-content\" href=\"#fs-id1169594157964\">(Example 11)<\/a>, we used the point\u2013slope form to find the equation. We could have looked at this in a different way.<\/p>\n<p id=\"fs-id1169596590476\">We want to find a line that is perpendicular to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dbaec542907415eac32615dfae0ae911_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>. The graph shows us the line<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/> and the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dbaec542907415eac32615dfae0ae911_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><span id=\"fs-id1169596360518\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is x equals 5 intercepts the x-axis at (5, 0) and runs parallel to the y-axis. Elsewhere on the graph, the point (3, 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_06_006_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is x equals 5 intercepts the x-axis at (5, 0) and runs parallel to the y-axis. Elsewhere on the graph, the point (3, negative 2) is plotted.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169594158800\">We know every line perpendicular to a vertical line is horizontal, so we will sketch the horizontal line through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dbaec542907415eac32615dfae0ae911_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><span id=\"fs-id1169594012432\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is x equals 5 intercepts the x-axis at (5, 0) and runs parallel to the y-axis. Elsewhere on the graph, the points (negative 2, negative 2), (0, negative 2), (3, negative 2), and (6, negative 2) are plotted. A line perpendicular to the previous line passes through those points and runs parallel to the x-axis.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_007_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is x equals 5 intercepts the x-axis at (5, 0) and runs parallel to the y-axis. Elsewhere on the graph, the points (negative 2, negative 2), (0, negative 2), (3, negative 2), and (6, negative 2) are plotted. A line perpendicular to the previous line passes through those points and runs parallel to the x-axis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596438830\">Do the lines appear perpendicular?<\/p>\n<p id=\"fs-id1169596363033\">If we look at a few points on this horizontal line, we notice they all have <em data-effect=\"italics\">y<\/em>-coordinates of <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;\" \/>. So, the equation of the line perpendicular to the vertical line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f986dbfac9d3f29a18cba91e9efa9d2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/>.<\/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-id1169596389098\" data-type=\"problem\">\n<p id=\"fs-id1169596389100\">Find an equation of a line that is perpendicular to <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;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ad41549099069a514e17dfbc399b6c68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p>Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<div id=\"fs-id1169596662202\" 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-id1169596662208\">The line <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;\" \/> is a horizontal line. Any line perpendicular to it must be vertical, in the form <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;\" \/>. Since the perpendicular line is vertical and passes through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ad41549099069a514e17dfbc399b6c68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>, every point on it has an <em data-effect=\"italics\">x<\/em>-coordinate of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/>. The equation of the perpendicular line is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b3dc975a98ccada6f136856736d7df06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: -1px;\" \/>. You may want to sketch the lines. Do they appear 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 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594176078\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1169596362956\" data-type=\"problem\">\n<p id=\"fs-id1169596362958\">Find an equation of a line that is perpendicular to the line <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;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb0e705487e4783110580c14181b9d4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope\u2013intercept form.<\/p>\n<\/div>\n<div id=\"fs-id1169596642217\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596642219\"><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;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594001983\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594001987\" data-type=\"exercise\">\n<div id=\"fs-id1169594001990\" data-type=\"problem\"><\/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 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594001990\" data-type=\"problem\">\n<p id=\"fs-id1169594001992\">Find an equation of a line that is perpendicular to the line <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;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3840972c083bab5f065585197b233498_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594151456\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594151458\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b3dc975a98ccada6f136856736d7df06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"media-2\" data-type=\"note\">\n<p id=\"fs-id1169596656043\">Access this online resource for additional instruction and practice with finding the equation of a line.<\/p>\n<ul id=\"fs-id1169596656047\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/25PointSlopeForm\">Use the Point-Slope 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-id1169596454747\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">To Find an Equation of a Line Given the Slope and a Point<\/strong>\n<ol id=\"fs-id1169596648396\" class=\"stepwise\" type=\"1\">\n<li>Identify the slope.<\/li>\n<li>Identify the point.<\/li>\n<li>Substitute the values into the point-slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<li>Write the equation in slope-intercept form.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">To Find an Equation of a Line Given Two Points<\/strong>\n<ol id=\"fs-id1169594175438\" class=\"stepwise\" type=\"1\">\n<li>Find the slope using the given points.<\/li>\n<li>Choose one point.<\/li>\n<li>Substitute the values into the point-slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<li>Write the equation in slope-intercept form.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">To Write and Equation of a Line<\/strong>\n<ul id=\"fs-id1169596642287\" data-bullet-style=\"open-circle\">\n<li>If given slope and <em data-effect=\"italics\">y<\/em>-intercept, use slope\u2013intercept 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;\" \/>.<\/li>\n<li>If given slope and a point, use point\u2013slope form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<li>If given two points, use point\u2013slope form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">To Find an Equation of a Line Parallel to a Given Line<\/strong>\n<ol id=\"fs-id1169594007902\" class=\"stepwise\" type=\"1\">\n<li>Find the slope of the given line.<\/li>\n<li>Find the slope of the parallel line.<\/li>\n<li>Identify the point.<\/li>\n<li>Substitute the values into the point-slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<li>Write the equation in slope-intercept form.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">To Find an Equation of a Line Perpendicular to a Given Line<\/strong>\n<ol id=\"fs-id1169596656200\" class=\"stepwise\" type=\"1\">\n<li>Find the slope of the given line.<\/li>\n<li>Find the slope of the perpendicular line.<\/li>\n<li>Identify the point.<\/li>\n<li>Substitute the values into the point-slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<li>Write the equation in slope-intercept form.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1 data-type=\"title\">Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1169594034186\">\n<dt>point\u2013slope form<\/dt>\n<dd id=\"fs-id1169594034192\">The point\u2013slope 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 containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-daf7d3000a611d6a6b02b6093c3dfb1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#44;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -4px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/dd>\n<\/dl>\n<\/div>\n<h1 data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1169596554445\">Find an Equation of the Line Given the Slope and <em data-effect=\"italics\">y<\/em>-Intercept<\/h2>\n<p id=\"fs-id1169596446288\">In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope\u2013intercept form.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\">\n<tbody>\n<tr>\n<td style=\"width: 49.9086%;\">1. slope 4 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<td style=\"width: 50.0914%;\">2. slope 3 and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6655aef23bcf82d48b1ff5bf888d5b2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#53;&#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: 49.9086%;\">3. slope 8 and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-76ba30a779b2946f1d9c14bf4ce7c710_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#54;&#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: 50.0914%;\">4. slope 6 and <em data-effect=\"italics\">y<\/em>-intercept <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;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">5. slope <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;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fd9b5c6abace2dbe781377a5ef9afd2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#55;&#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: 50.0914%;\">6. slope <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;\" \/> 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<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">7. slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" 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-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;\" \/><\/td>\n<td style=\"width: 50.0914%;\">8. slope <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 <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-017f20ea0c6fda3470cedb20ea0b5537_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">9. slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e174a73678f6bd6f70d7aaec8f911349_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5f6ab1a0ed415088c10eaaa3977a4992_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#53;&#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: 50.0914%;\">10. slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-56fd13ae94393ab95b21e4d3651f1ec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> 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;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">11. slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c7d25e8c067ff3ef20a88a636c72c473_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"22\" style=\"vertical-align: -6px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-017f20ea0c6fda3470cedb20ea0b5537_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#51;&#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: 50.0914%;\">12. slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aa266d939635a899a53c3c9df44a7ef9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"22\" style=\"vertical-align: -6px;\" \/> 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<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">13. slope 0 and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-398828550549fdd4b2191f8f7cde7bd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#50;&#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: 50.0914%;\">14. slope 0 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;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">15. slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" 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-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#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: 50.0914%;\">16. slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" 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-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596653337\">In the following exercises, find the equation of the line shown in each graph. Write the equation in slope\u2013intercept form.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50.0914%;\"><span id=\"fs-id1169596253307\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, 0) is plotted. A line intercepts the y-axis at (0, 4) and intercepts the x-axis at (2, 0).\">17. <img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_202_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, 0) is plotted. A line intercepts the y-axis at (0, 4) and intercepts the x-axis at (2, 0).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.9086%;\"><span id=\"fs-id1169596653346\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (1, negative 2) is plotted. A line intercepts the y-axis at (0, negative 5), passes through the point (1, negative 2), and intercepts the x-axis at (5 thirds, 0).\">18. <img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_201_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (1, negative 2) is plotted. A line intercepts the y-axis at (0, negative 5), passes through the point (1, negative 2), and intercepts the x-axis at (5 thirds, 0).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\"><span id=\"fs-id1169596649047\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (4, 5) is plotted. A line intercepts the x-axis at (negative 8 thirds, 0), intercepts the y-axis at (0, 2), and passes through the point (4, 5).\">19. <img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_204_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (4, 5) is plotted. A line intercepts the x-axis at (negative 8 thirds, 0), intercepts the y-axis at (0, 2), and passes through the point (4, 5).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.9086%;\"><span id=\"fs-id1169596446363\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (6, 0) is plotted. A line intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (6, 0).\">20. <img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_203_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (6, 0) is plotted. A line intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (6, 0).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\"><span id=\"fs-id1169596369564\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, negative 4) is plotted. A line intercepts the x-axis at (negative 2 thirds, 0), intercepts the y-axis at (0, negative 1), and passes through the point (2, negative 4).\">21. <img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_206_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, negative 4) is plotted. A line intercepts the x-axis at (negative 2 thirds, 0), intercepts the y-axis at (0, negative 1), and passes through the point (2, negative 4).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.9086%;\"><span id=\"fs-id1169596697233\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (3, negative 1) is plotted. A line intercepts the y-axis at (0, 2), intercepts the x-axis at (9 fourths, 0), and passes through the point (3, negative 1).\">22. <img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_205_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (3, negative 1) is plotted. A line intercepts the y-axis at (0, 2), intercepts the x-axis at (9 fourths, 0), and passes through the point (3, negative 1).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\"><span id=\"fs-id1169596446489\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (negative 3, 6) is plotted. A line running parallel to the x-axis passes through (negative 3, 6) and intercepts the y-axis at (0, 6).\">23. <img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_208_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (negative 3, 6) is plotted. A line running parallel to the x-axis passes through (negative 3, 6) and intercepts the y-axis at (0, 6).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.9086%;\"><span id=\"fs-id1169596387068\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, negative 2) is plotted. A line running parallel to the x-axis intercepts the y-axis at (0, negative 2) and passes through the point (2, negative 2).\">24. <img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_04_06_207_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, negative 2) is plotted. A line running parallel to the x-axis intercepts the y-axis at (0, negative 2) and passes through the point (2, negative 2).\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596658352\">Find an Equation of the Line Given the Slope and a Point<\/h2>\n<p id=\"fs-id1169596658358\">In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope\u2013intercept form.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\">\n<tbody>\n<tr>\n<td style=\"width: 49.7258%;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a8b82325f71fc38caff7934aaf42cb52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -6px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d9b49b201a3efa56726407933e068d18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#50;&#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: 50.2742%;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70409291bbfc6e902ed9eb47c2da8cc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -6px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38f47676ff4305b6e1df48d364862ed0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#51;&#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: 49.7258%;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2eabe083d9f31fe4ea2aa67deab979e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -6px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27acd60b4851baa3fac77a6a37f24296_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#55;&#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: 50.2742%;\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b04a7ed5e9e732e0ab4e87388155f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -6px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc9db18ceda8b325515059e9c425b44f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#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: 49.7258%;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9589ef5f4f89ddd56712778939e249f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-064fbe5b13d7774ef232dcf1aebc3fa5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.2742%;\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1c682827dbbd6233dceaa20c8d888f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8781692f7fffdf9ddfd97a6c49cb6935_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6fae7ea410efdec23083d9f11b3cee98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3759239cc8a8b79fea64487a1920f46d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#44;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.2742%;\">32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-89c82be9317e7136f63c6bf503e5a423_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9dc0222817b1b6ae6a403e97e1993c39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">33. Horizontal line containing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b098ad691d3b1e66796376e6000e2385_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.2742%;\">34. Horizontal line containing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-edd8d8b57c2815309edbd447803c95fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">35. Horizontal line containing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6eb713a032efe6d2cd357cc2ab12b55a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.2742%;\">36. Horizontal line containing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e6b25c6279fe53efe7c78796a156eeed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4ed45e794f3aaa62fad31f963f6c4fff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0079e38fdd16e43ef7a238df2ab245d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.2742%;\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-efd064b48d98160a6fb439eefec18afa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ebe785a1a1f173c2cb47dc17a15cdc63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-754283866fe7f24eadf016df34fe5cf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: -1px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e6b25c6279fe53efe7c78796a156eeed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.2742%;\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3fea9415255c2302e26041feaad8e47f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: 0px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-659f5d2dee5bcea4b83fdb4d330c9b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.7258%;\">41. Horizontal line containing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22807f5b7dd745b2825d8e7373202547_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#56;&#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: 50.2742%;\">42. Horizontal line containing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1564d1d2328bb6bd9e7b30e6d573d2fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169594087053\">Find an Equation of the Line Given Two Points<\/h2>\n<p id=\"fs-id1169594087059\">In the following exercises, find the equation of a line containing the given points. Write the equation in slope\u2013intercept form.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\">\n<tbody>\n<tr>\n<td style=\"width: 49.9086%;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4307e3633578c7e56f8f767895b20497_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#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-2da1eb750fc283f55cb9396d5536b47a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#53;&#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: 50.0914%;\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-80be894898c77ffda9d4d5843e6791f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#54;&#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-159ccfbcee3ed270fafd4d79974b76e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#51;&#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: 49.9086%;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-81a55cc5621f60401efb29cbe743e855_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#55;&#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-aa1e37a09fb9a2a365196b061a17f1fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#56;&#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: 50.0914%;\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b1804935101b0791adf13cb00d6ac306_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#51;&#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-9eb44641a2132855d0bc4176e9a177ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#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: 49.9086%;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb242707b07d2123762ae0b5253ad3ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-84e35e40e916e50503f09b25572279f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#54;&#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: 50.0914%;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9523da542e5bfc81814e047c926984c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f0328eefa827aa872d814dd392d0d7e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1c6d0c0591d57104498832e4e3a741a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2aed587169d8783cf3e545c652f3751c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">50. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f2347704000ad2e9ae878a8427611b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4c54443702950a02530914c1301929f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#44;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dbaec542907415eac32615dfae0ae911_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#50;&#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-6bd03bb09a34e49dd9f3ebf548e3dab1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">52. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb87bfe9ba69a89c4ac12d88180c12e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#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-edd8d8b57c2815309edbd447803c95fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">53. <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;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb242707b07d2123762ae0b5253ad3ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">54. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e2c3a69d33f9737210f9c4f1551f4b9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#52;&#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-1564d1d2328bb6bd9e7b30e6d573d2fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb6560ec04491f4e7cf02e14e6df5ec3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#50;&#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-9a73c1812707ce5b0b7341d06a667a00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#51;&#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: 50.0914%;\">56. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5f3a1814d4c4364566cfa9f7341421fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#44;&#50;&#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-c916d60aa47fa4acda0a60cfa203c36b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#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<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ecc91b8d5e91ea23c08fcf2ee52342c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-59362f5af96d469003752c4e94766b84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1eef27e4ca86fffdc9c79bdabd347e5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ccc35b92a6567ced556cb46473589564_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#50;&#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-1f307aa6b65fb69739e6c2b7458409de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc9db18ceda8b325515059e9c425b44f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#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-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: 49.9086%;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a7b90c027eccd1d5f6de21196682699_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-659f5d2dee5bcea4b83fdb4d330c9b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-abcb6ace4b542ff0928998579e86da44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#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-12aeb9559a0d3673fa3759c68e52b96b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#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-3ab73a57c5e039ffb22ed1a8e29747bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#52;&#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: 50.0914%;\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b1804935101b0791adf13cb00d6ac306_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#51;&#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-52a836a9aba870ffb4036b68b4cb0c99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#48;&#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: 49.9086%;\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7ba9cc2a7f12e65a6b3de8f34bcc16e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4f1459d65082a141f08f1b02c9ef56ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e6b25c6279fe53efe7c78796a156eeed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb202e0826326eae1d4751969417d175_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.9086%;\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8c1fb7b2aa4d3e58c5af2d13706f56d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#53;&#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-686bfba4a3f51fc9d2a456d575265a40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.0914%;\">68. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-04a01c6262a6fba997fa24381bda331d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#45;&#49;&#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-8781692f7fffdf9ddfd97a6c49cb6935_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169594239500\">Find an Equation of a Line Parallel to a Given Line<\/h2>\n<p id=\"fs-id1169594239506\">In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope\u2013intercept form.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\">\n<tbody>\n<tr>\n<td style=\"width: 49.543%;\">69. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-57e4c937afc59ff88a5b8f1c36e732ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2da1eb750fc283f55cb9396d5536b47a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#53;&#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: 50.457%;\">70. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a75f766ee596494054c74bdbb0f98fb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ce830c2dfa3b70e2906cf4d1b7248973_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#50;&#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: 49.543%;\">71. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-64c61b5034010d35abb6efee026ea5bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1564d1d2328bb6bd9e7b30e6d573d2fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#51;&#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: 50.457%;\">72. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b754ae8eb949f8f8d85ba36ebabb52d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f2347704000ad2e9ae878a8427611b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.543%;\">73. line <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;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-28a186f2424d2e935d6aa6388441b6d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#48;&#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: 50.457%;\">74. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a63f2d92b5ed8cad7ba04e514955e9b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#121;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4307e3633578c7e56f8f767895b20497_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#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: 49.543%;\">75. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-07795f3421886c79416fa26cd22cc5f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6655aef23bcf82d48b1ff5bf888d5b2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#53;&#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: 50.457%;\">76. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5de4c0bb354c832de12ef224ed69a7d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-017f20ea0c6fda3470cedb20ea0b5537_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.543%;\">77. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b3dc975a98ccada6f136856736d7df06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: -1px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0bd0b31c672d6277d527b16652fb255d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50.457%;\">78. line <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;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef9b0ead245d0b508218b1cb59d48442_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.543%;\">79. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-04f92a339068c01b544cfb963e667ba0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#54;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" style=\"vertical-align: 0px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9a73c1812707ce5b0b7341d06a667a00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#51;&#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: 50.457%;\">80. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e0aacb848a27943fc0e8fba70f545d78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#50;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" style=\"vertical-align: 0px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a685e6a8556e8135bece1243dc70fe1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#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<\/tr>\n<tr>\n<td style=\"width: 49.543%;\">81. line <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;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-abcb6ace4b542ff0928998579e86da44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#52;&#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: 50.457%;\">82. line <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;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8fbb5d034d8bc7481119846ba5facddb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#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<\/tr>\n<tr>\n<td style=\"width: 49.543%;\">83. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23717c9f5cff43e836ac20cffb06f6b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#55;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"72\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c3ac38dbb39343c28a60a287dfb114b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#45;&#49;&#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: 50.457%;\">84. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00b7e2b25eedab07072cbadca87156ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#50;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f054d79e93ab302f68adcad7d4c3ec21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169594154482\">Find an Equation of a Line Perpendicular to a Given Line<\/h2>\n<p id=\"fs-id1169596445758\">In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope\u2013intercept form.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 112px;\">\n<tbody>\n<tr>\n<td style=\"width: 51.3711%;\">85. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e39248f0d5cb50d2abf7ba8a19a9833_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c4a2258b08828b82f5478b79177f57c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#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: 48.6289%;\">86. line <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;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f78f604644c2cdddbea2fc4d8ad49cca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#50;&#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: 51.3711%;\">87. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a715197fb7403b90b68b81fbc750b686_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"85\" style=\"vertical-align: -6px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d5b80bc57d91ba9e2936cc72d75618b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#52;&#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: 48.6289%;\">88. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6c8231fcdf97865da2a7696f96820b86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-862a9525ac8db19009bf877fff4597b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.3711%;\">89. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e1fd974603963c220d47ea6de0ff3640_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#51;&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1f307aa6b65fb69739e6c2b7458409de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 48.6289%;\">90. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e3d5dfb481073534f07053cb2c0379d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#51;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6de38faced02869069c306c45a22c5e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.3711%;\">91. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0c01cba79f5f71538c5d63bcdf8f8449_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#53;&#121;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"105\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#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: 48.6289%;\">92. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-091222f95283f716d5bf9c2f3b12eb8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#53;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#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: 51.3711%;\">93. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-577a53e3db0d698b0cdc80f784a050aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#54;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb242707b07d2123762ae0b5253ad3ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 48.6289%;\">94. line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2d5f7756bdb439826b55402e8147dd5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#51;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ecc91b8d5e91ea23c08fcf2ee52342c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.3711%;\">95. line <em data-effect=\"italics\">y<\/em>-axis, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb160c5e6177bdd7a1d220c410258e5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#49;&#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: 48.6289%;\">96. line <em data-effect=\"italics\">y<\/em>-axis, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aecc845ff8fcecb422091e6436adca8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Mixed Practice<\/h2>\n<p id=\"fs-id1169596662267\">In the following exercises, find the equation of each line. Write the equation in slope\u2013intercept form.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\">\n<tbody>\n<tr>\n<td style=\"width: 50.0914%;\">97. Containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-81a55cc5621f60401efb29cbe743e855_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#55;&#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-aa1e37a09fb9a2a365196b061a17f1fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#56;&#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: 49.7258%;\">98. Containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b1804935101b0791adf13cb00d6ac306_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#51;&#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-9eb44641a2132855d0bc4176e9a177ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#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%;\">99. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2eabe083d9f31fe4ea2aa67deab979e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -6px;\" \/>, containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27acd60b4851baa3fac77a6a37f24296_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#55;&#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: 49.7258%;\">100. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b04a7ed5e9e732e0ab4e87388155f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -6px;\" \/>, containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc9db18ceda8b325515059e9c425b44f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#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%;\">101. Parallel to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-07795f3421886c79416fa26cd22cc5f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>, containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6655aef23bcf82d48b1ff5bf888d5b2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#53;&#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: 49.7258%;\">102. Parallel to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5de4c0bb354c832de12ef224ed69a7d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>, containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-017f20ea0c6fda3470cedb20ea0b5537_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">103. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9589ef5f4f89ddd56712778939e249f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/>, containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-064fbe5b13d7774ef232dcf1aebc3fa5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.7258%;\">104. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1c682827dbbd6233dceaa20c8d888f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/>, containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8781692f7fffdf9ddfd97a6c49cb6935_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">105. Perpendicular to the line <em data-effect=\"italics\">y<\/em>-axis, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-551477e8eec13715fc061945ccc1b984_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.7258%;\">106. Perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-182fc92f40a7dcdeb73c1e9f3b2b4c00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#49;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\" \/>, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b61914c33c0ffe75331208eaa502d627_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">107. Containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd6f8f312ab67ad0422a4959540654f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a17ffffadfb8456567f4803e943d15a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.7258%;\">108. Containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b1804935101b0791adf13cb00d6ac306_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#51;&#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-9eb44641a2132855d0bc4176e9a177ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#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%;\">109. Parallel to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b3dc975a98ccada6f136856736d7df06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: -1px;\" \/>, containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0bd0b31c672d6277d527b16652fb255d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.7258%;\">110. Parallel to the line <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;\" \/>, containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef9b0ead245d0b508218b1cb59d48442_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">111. Containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb242707b07d2123762ae0b5253ad3ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-84e35e40e916e50503f09b25572279f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#54;&#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: 49.7258%;\">112. Containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9523da542e5bfc81814e047c926984c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c02ba61efe13be423bc75f83a9846930_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">113. Perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0e5650ba573829a8aeeb87aec3a5d6a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#51;&#121;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\" \/>, containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#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: 49.7258%;\">114. Perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0f592894dfc669be1583facabdf7c38b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#50;&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/>, containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-627391f2fad7216057fc57692a374893_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"material-set-2\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<h2 id=\"fs-id1169594008368\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 51.1883%;\">115. <strong>Fuel consumption.<\/strong> The city mpg, <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 highway mpg, <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;\" \/>, of two cars are given by the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e50087828b6c78231e66f37150e3d06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#57;&#44;&#52;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/> and<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b71263d300f589f9f46adb05d6c81cab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#57;&#44;&#50;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/>. Find a linear equation that models the relationship between city mpg and highway mpg.<\/td>\n<td style=\"width: 48.8117%;\">116. <strong>Cholesterol.<\/strong> The age, <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 LDL cholesterol level, <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;\" \/>, of two men are given by the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f070f0e322e364995b613fb5be477987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#56;&#44;&#54;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f0c9112f1cdb2afbbc45b9a637e10d69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#55;&#44;&#49;&#50;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/>. Find a linear equation that models the relationship between age and LDL cholesterol level.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 67.2761%;\">117. Explain in your own words why the slopes of two perpendicular lines must have opposite signs.<\/td>\n<td style=\"width: 32.724%;\">118. Why are all horizontal lines parallel?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 481px;\">\n<tbody>\n<tr>\n<td style=\"width: 48.4461%;\">1. <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;\" \/><\/td>\n<td style=\"width: 51.5539%;\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-39eddb60f607ec62514344db7a8ca251_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#56;&#120;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-daa835aa0165b26ed55aa040687091ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-64c61b5034010d35abb6efee026ea5bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-31c3a332e84de5f26efdd3b93c76dac1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-913e68ca5babd313dba82870f28de6c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-552d8ed773e160e229551b39aff39445_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d6dd00142930f9fde84a1aaca1dedc3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-909c05e0f55b7e4ded8427ffa3095b15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-42b4179737f7f7cbebbd260ce5834eb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d91058290d7ee3b2111a3e8cd88ba803_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"99\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17932c1f62fa0296571e88ce8fc0a117_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7452964cda1730f10485c1f3ec30cf72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e40d21b2bfcfec835bbefa4e55b778f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f139e4c1029ae94acd19b16b22fe685a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3bab6b2f4b527915db5f8294dcbe8c77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#120;&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"106\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">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: 51.5539%;\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c15f100d859ec9077a43994ca473b018_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4d359fdaffc0eca07a4f7a895d6c14f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;&#120;&#45;&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"106\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7845764314e76e27fd32be32cf145e15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;&#120;&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">41. <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;\" \/><\/td>\n<td style=\"width: 51.5539%;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f781be88cbf76817b3d211a8f4f966b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;&#120;&#43;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"105\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-163b224753499045192328b2815e4ac7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f5873a09309e9666b2777fd6c411db4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da0db1179deea5fc9fc85a57bbda1606_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#55;&#120;&#43;&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-197b94fcb3a0526405c278fd07fc591d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#55;&#125;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bba8edb9bee0c90c97834d793b9002d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2145acc2878ed61214887e120f2485b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\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-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;\" \/><\/td>\n<td style=\"width: 51.5539%;\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-552d8ed773e160e229551b39aff39445_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/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-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<td style=\"width: 51.5539%;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3830f1c4beca3ad0dd7e3a5dae581de2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" 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-dc5af659ead7b0a2c4a51b4abb0e74fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">67. <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: 48.4461%;\">69. <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<td style=\"width: 51.5539%;\">71. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-67d9eb53c924775e8773609191330c21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" 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-fe73296a6eb057f3b8df5137955f8bdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9268118e40788cd353d106224f03d82e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/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-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: 51.5539%;\">79. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2145acc2878ed61214887e120f2485b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: -1px;\" \/><\/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-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;\" \/><\/td>\n<td style=\"width: 51.5539%;\">83. <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<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">85. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0a99c26c04ea6299b78366ce136d5675_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">87. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-42b07f88ea6395ef864a9f4ae63ca7a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">89. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-733c7e253d073d08ab36823fb121492a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">91. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d0064de2d84f9523ea481233448917a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">93. <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;\" \/><\/td>\n<td style=\"width: 51.5539%;\">95. <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;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">97. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-163b224753499045192328b2815e4ac7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">99. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e40d21b2bfcfec835bbefa4e55b778f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">101. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9268118e40788cd353d106224f03d82e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">103. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f139e4c1029ae94acd19b16b22fe685a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">105. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-552d8ed773e160e229551b39aff39445_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">107. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9573bcdc8144ab85298374bd51ec886d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">109. <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: 51.5539%;\">111. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f5873a09309e9666b2777fd6c411db4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">113. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-95ee29fa8ebf828c73cdbd551e17d11b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 51.5539%;\">115. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2e87ced9940fa05d4c0d3c089fc10b5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#49;&#46;&#50;&#120;&#43;&#53;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 48.4461%;\">117. Answers will vary.<\/td>\n<td style=\"width: 51.5539%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cFind the 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":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1844","chapter","type-chapter","status-publish","hentry"],"part":1370,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1844","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\/1844\/revisions"}],"predecessor-version":[{"id":1845,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1844\/revisions\/1845"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/1370"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1844\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=1844"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1844"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=1844"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=1844"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}