{"id":906,"date":"2020-08-07T19:03:31","date_gmt":"2020-08-07T19:03:31","guid":{"rendered":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/graph-linear-equations-in-two-variables-3\/"},"modified":"2021-08-31T21:19:40","modified_gmt":"2021-08-31T21:19:40","slug":"graph-linear-equations-in-two-variables-3","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/graph-linear-equations-in-two-variables-3\/","title":{"raw":"3.2 Graph Linear Equations in Two Variables","rendered":"3.2 Graph Linear Equations in Two Variables"},"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 it is expected that you will be able to:\n<ul>\n \t<li>Recognize the relationship between the solutions of an equation and its graph.<\/li>\n \t<li>Graph a linear equation by plotting points.<\/li>\n \t<li>Graph vertical and horizontal lines.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Recognize the Relationship Between the Solutions of an Equation and its Graph<\/h1>\n<p id=\"fs-id1169596288680\">In the previous section, we found several solutions to the equation \\(3x+2y=6\\). They are listed in the table below. So, the ordered pairs \\(\\left(0,3\\right)\\), \\(\\left(2,0\\right)\\), and \\(\\left(1,\\dfrac{3}{2}\\right)\\) are some solutions to the equation \\(3x+2y=6\\). We can plot these solutions in the rectangular coordinate system as shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_001\">(Figure 1)<\/a>.<\/p>\n\n<table class=\"aligncenter\" style=\"height: 80px;\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation 3x plus 2y equals 6. The second row is a header row and it labels each column. The first column header is \u201cx\u201d, the second is \u201cy\u201d and the third is \u201c(x, y)\u201d. Under the first column are the numbers 0, 2, and 1. Under the second column are the numbers 3, 0, and three halves. Under the third column are the ordered pairs (0, 3), (2, 0), and (1, three halves).\"><caption>\\(3x+2y=6\\)<\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"height: 16px; width: 38.9062px;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"height: 16px; width: 132.906px;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"height: 16px; width: 238.906px;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"height: 16px; width: 38.9062px;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"height: 16px; width: 132.906px;\" data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td style=\"height: 16px; width: 238.906px;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(0,3\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"height: 16px; width: 38.9062px;\" data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td style=\"height: 16px; width: 132.906px;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"height: 16px; width: 238.906px;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(2,0\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"height: 16px; width: 38.9062px;\" data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td style=\"height: 16px; width: 132.906px;\" data-valign=\"middle\" data-align=\"center\">\\(\\dfrac{3}{2}\\)<\/td>\n<td style=\"height: 16px; width: 238.906px;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(1,\\dfrac{3}{2}\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div><\/div>\n<div id=\"CNX_ElemAlg_Figure_04_02_001\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"301\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2020\/08\/CNX_ElemAlg_Figure_04_02_001_img_new.jpg\" alt=\"A graph that plots the points (0, 3), (1, three halves), and (2, 0).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"> Figure .1[\/caption]\n\n<\/div>\n<p id=\"fs-id1169596395639\">Notice how the points line up perfectly? We connect the points with a line to get the graph of the equation \\(3x+2y=6\\). See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_002\">(Figure 2)<\/a>. Notice the arrows on the ends of each side of the line. These arrows indicate the line continues.<\/p>\n\n<div id=\"CNX_ElemAlg_Figure_04_02_002\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"301\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_002_img_new.jpg\" alt=\"Described in previous paragraph.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"> Figure .2[\/caption]\n\n<\/div>\n<p id=\"fs-id1169596498779\">Every point on the line is a solution of the equation. Also, every solution of this equation is a point on this line. Points <em data-effect=\"italics\">not<\/em> on the line are not solutions.<\/p>\n<p id=\"fs-id1169596621603\">Notice that the point whose coordinates are \\(\\left(-2,6\\right)\\) is on the line shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_003\">(Figure 3)<\/a>. If you substitute \\(x=-2\\) and \\(y=6\\) into the equation, you find that it is a solution to the equation.<\/p>\n\n<div id=\"CNX_ElemAlg_Figure_04_02_003\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"301\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_003_img_new.jpg\" alt=\"Graphs the equation 3x plus 2y equals 6. The points (negative 2, 6) and (4, 1) are plotted. The line goes through (\u22122, 6) but not (4, 1).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"> Figure .3[\/caption]\n\n<\/div>\n<span id=\"fs-id1169596295719\" data-type=\"media\" data-alt=\"The figure shows a series of equations to check if the ordered pair (negative 2, 6) is a solution to the equation 3x plus 2y equals 6. The first line states \u201cTest (negative 2, 6)\u201d. The negative 2 is colored blue and the 6 is colored red. The second line states the two- variable equation 3x plus 2y equals 6. The third line shows the ordered pair substituted into the two- variable equation resulting in 3(negative 2) plus 2(6) equals 6 where the negative 2 is colored blue to show it is the first component in the ordered pair and the 6 is red to show it is the second component in the ordered pair. The fourth line is the simplified equation negative 6 plus 12 equals 6. The fifth line is the further simplified equation 6equals6. A check mark is written next to the last equation to indicate it is a true statement and show that (negative 2, 6) is a solution to the equation 3x plus 2y equals 6.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_020_img_new.jpg\" alt=\"The figure shows a series of equations to check if the ordered pair (negative 2, 6) is a solution to the equation 3x plus 2y equals 6. The first line states \u201cTest (negative 2, 6)\u201d. The negative 2 is colored blue and the 6 is colored red. The second line states the two- variable equation 3x plus 2y equals 6. The third line shows the ordered pair substituted into the two- variable equation resulting in 3(negative 2) plus 2(6) equals 6 where the negative 2 is colored blue to show it is the first component in the ordered pair and the 6 is red to show it is the second component in the ordered pair. The fourth line is the simplified equation negative 6 plus 12 equals 6. The fifth line is the further simplified equation 6equals6. A check mark is written next to the last equation to indicate it is a true statement and show that (negative 2, 6) is a solution to the equation 3x plus 2y equals 6.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596704533\">So the point \\(\\left(-2,6\\right)\\) is a solution to the equation \\(3x+2y=6\\). (The phrase \u201cthe point whose coordinates are \\(\\left(-2,6\\right)\\)\u201d is often shortened to \u201cthe point \\(\\left(-2,6\\right)\\).\u201d)<\/p>\n<span id=\"fs-id1169596233549\" data-type=\"media\" data-alt=\"The figure shows a series of equations to check if the ordered pair (4, 1) is a solution to the equation 3x plus 2y equals 6. The first line states \u201cWhat about (4, 1)?\u201d. The 4 is colored blue and the 1 is colored red. The second line states the two- variable equation 3x plus 2y equals 6. The third line shows the ordered pair substituted into the two- variable equation resulting in 3(4) plus 2(1) equals 6 where the 4 is colored blue to show it is the first component in the ordered pair and the 1 is red to show it is the second component in the ordered pair. The fourth line is the simplified equation 12 plus 2 equals 6. A question mark is placed above the equals sign to indicate that it is not known if the equation is true or false. The fifth line is the further simplified statement 14 not equal to 6. A \u201cnot equals\u201d sign is written between the two numbers and looks like an equals sign with a forward slash through it.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_021_img_new.jpg\" alt=\"The figure shows a series of equations to check if the ordered pair (4, 1) is a solution to the equation 3x plus 2y equals 6. The first line states \u201cWhat about (4, 1)?\u201d. The 4 is colored blue and the 1 is colored red. The second line states the two- variable equation 3x plus 2y equals 6. The third line shows the ordered pair substituted into the two- variable equation resulting in 3(4) plus 2(1) equals 6 where the 4 is colored blue to show it is the first component in the ordered pair and the 1 is red to show it is the second component in the ordered pair. The fourth line is the simplified equation 12 plus 2 equals 6. A question mark is placed above the equals sign to indicate that it is not known if the equation is true or false. The fifth line is the further simplified statement 14 not equal to 6. A \u201cnot equals\u201d sign is written between the two numbers and looks like an equals sign with a forward slash through it.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596211761\">So \\(\\left(4,1\\right)\\) is not a solution to the equation \\(3x+2y=6\\). Therefore, the point \\(\\left(4,1\\right)\\) is not on the line. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_002\">(Figure 2)<\/a>. This is an example of the saying, \u201cA picture is worth a thousand words.\u201d The line shows you <em data-effect=\"italics\">all<\/em> the solutions to the equation. Every point on the line is a solution of the equation. And, every solution of this equation is on this line. This line is called the <em data-effect=\"italics\">graph<\/em> of the equation \\(3x+2y=6\\).<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Graph of a linear equation<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169594086156\">The <span data-type=\"term\">graph of a linear equation<\/span> \\(Ax+By=C\\) is a line.<\/p>\n\n<ul id=\"fs-id1169596469070\" data-bullet-style=\"bullet\">\n \t<li>Every point on the line is a solution of the equation.<\/li>\n \t<li>Every solution of this equation is a point on this line.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596301929\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596364071\" data-type=\"exercise\">\n<div id=\"fs-id1169596232522\" data-type=\"problem\">\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-id1169596446085\" data-type=\"problem\">\n<p id=\"fs-id1169596590486\">The graph of \\(y=2x-3\\) is shown.<\/p>\n<span data-type=\"media\" data-alt=\"The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line has a positive slope and goes through the y-axis at the (0, negative 3). The line is labeled with the equation y equals 2x negative 3.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_004_img_new.jpg\" alt=\"Graphs the line 2x\u22123.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169594147325\">For each ordered pair, decide:<\/p>\n<p id=\"fs-id1168464057467\"><span class=\"token\">a)<\/span>\u00a0Is the ordered pair a solution to the equation?<span data-type=\"newline\">\n<\/span>b) Is the point on the line?<\/p>\n<p id=\"fs-id1169594053219\">A \\(\\left(0,-3\\right)\\)\u2003B \\(\\left(3,3\\right)\\)\u2003C \\(\\left(2,-3\\right)\\)\u2003D \\(\\left(-1,-5\\right)\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1169596584660\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\">\n\n<strong>Solution<\/strong>\n\n<\/div>\n<p id=\"fs-id1169594031478\">Substitute the <em data-effect=\"italics\">x<\/em>- and <em data-effect=\"italics\">y<\/em>- values into the equation to check if the ordered pair is a solution to the equation.<\/p>\n<span class=\"token\">a)<\/span><span data-type=\"newline\">\n<\/span><span id=\"fs-id1169594053171\" data-type=\"media\" data-alt=\"The figure shows a series of equations to check if the ordered pairs (0, negative 3), (3, 3), (2, negative 3), and (negative 1, negative 5) are a solutions to the equation y equals 2x negative 3. The first line states the ordered pairs with the labels A: (0, negative 3), B: (3, 3), C: (2, negative 3), and D: (negative 1, negative 5). The first components are colored blue and the second components are colored red. The second line states the two- variable equation y equals 2x minus 3. The third line shows the four ordered pairs substituted into the two- variable equation resulting in four equations. The first equation is negative 3 equals 2(0) minus 3 where the 0 is colored clue and the negative 3 on the left side of the equation is colored red. The second equation is 3 equals 2(3) minus 3 where the 3 in parentheses is colored clue and the 3 on the left side of the equation is colored red. The third equation is negative 3 equals 2(2) minus 3 where the 2 in parentheses is colored clue and the negative 3 on the left side of the equation is colored red. The fourth equation is negative 5 equals 2(negative 1) minus 3 where the negative 1 is colored clue and the negative 5 is colored red. Question marks are placed above all the equal signs to indicate that it is not known if the equations are true or false. The fourth line shows the simplified versions of the four equations. The first is negative 3 equals negative 3 with a check mark indicating (0, negative 3) is a solution. The second is 3 equals 3 with a check mark indicating (3, 3) is a solution. The third is negative 3 not equals 1 indicating (2, negative 3) is not a solution. The fourth is negative 5 equals negative 5 with a check mark indicating (negative 1, negative 5) is a solution.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_022_img_new.jpg\" alt=\"The figure shows a series of equations to check if the ordered pairs (0, negative 3), (3, 3), (2, negative 3), and (negative 1, negative 5) are a solutions to the equation y equals 2x negative 3. The first line states the ordered pairs with the labels A: (0, negative 3), B: (3, 3), C: (2, negative 3), and D: (negative 1, negative 5). The first components are colored blue and the second components are colored red. The second line states the two- variable equation y equals 2x minus 3. The third line shows the four ordered pairs substituted into the two- variable equation resulting in four equations. The first equation is negative 3 equals 2(0) minus 3 where the 0 is colored clue and the negative 3 on the left side of the equation is colored red. The second equation is 3 equals 2(3) minus 3 where the 3 in parentheses is colored clue and the 3 on the left side of the equation is colored red. The third equation is negative 3 equals 2(2) minus 3 where the 2 in parentheses is colored clue and the negative 3 on the left side of the equation is colored red. The fourth equation is negative 5 equals 2(negative 1) minus 3 where the negative 1 is colored clue and the negative 5 is colored red. Question marks are placed above all the equal signs to indicate that it is not known if the equations are true or false. The fourth line shows the simplified versions of the four equations. The first is negative 3 equals negative 3 with a check mark indicating (0, negative 3) is a solution. The second is 3 equals 3 with a check mark indicating (3, 3) is a solution. The third is negative 3 not equals 1 indicating (2, negative 3) is not a solution. The fourth is negative 5 equals negative 5 with a check mark indicating (negative 1, negative 5) is a solution.\" data-media-type=\"image\/jpeg\"><\/span>\n\nb) Plot the points A \\(\\left(0,3\\right)\\), B \\(\\left(3,3\\right)\\), C \\(\\left(2,-3\\right)\\), and D \\(\\left(-1,-5\\right)\\).<span data-type=\"newline\">\n<\/span> <span id=\"fs-id1169594085144\" data-type=\"media\" data-alt=\"The figure shows a straight line and four points and on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the two points and are labeled by the coordinates (negative 1, negative 5), (0, negative 3), (2, negative 3), and (3, 3). The straight line, labeled with the equation y equals 2x negative 3 goes through the three points (negative 1, negative 5), (0, negative 3), and (3, 3) but does not go through the point (2, negative 3).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_005_img_new.jpg\" alt=\"Graph of the equation 2x\u22123. The points described in the previous paragraph are plotted.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596380866\">The points \\(\\left(0,3\\right)\\), \\(\\left(3,3\\right)\\), and \\(\\left(-1,-5\\right)\\) are on the line \\(y=2x-3\\), and the point \\(\\left(2,-3\\right)\\) is not on the line.<\/p>\n<p id=\"fs-id1169596307156\">The points that are solutions to \\(y=2x-3\\) are on the line, but the point that is not a solution is not on the 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 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596301929\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596364071\" data-type=\"exercise\">\n<div id=\"fs-id1169596232522\" data-type=\"problem\">\n<p id=\"fs-id1169596679540\">Use the graph of \\(y=3x-1\\) to decide whether each ordered pair is:<\/p>\n\n<ul id=\"fs-id1169596240370\" data-bullet-style=\"bullet\">\n \t<li>a solution to the equation.<\/li>\n \t<li>on the line.<\/li>\n<\/ul>\n<p id=\"fs-id1169596497114\"><span class=\"token\">a) <\/span>\\(\\left(0,-1\\right)\\)\u2003b) \\(\\left(2,5\\right)\\)<\/p>\n<span id=\"fs-id1169596375599\" data-type=\"media\" data-alt=\"The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the point (negative 2, negative 7) and for every 3 units it goes up, it goes one unit to the right. The line is labeled with the equation y equals 3x minus 1.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_006_img_new.jpg\" alt=\"Graph of the equation y = 3x\u22121.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id1169596446214\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596497874\"><span class=\"token\">a)<\/span> yes, yes\u2003b) yes, yes<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596243367\" class=\"bc-section section\" data-depth=\"1\">\n<h1 data-type=\"title\">Graph a Linear Equation by Plotting Points<\/h1>\n<p id=\"fs-id1169596531943\">There are several methods that can be used to graph a linear equation. The method we used to graph \\(3x+2y=6\\) is called plotting points, or the Point\u2013Plotting Method.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How To Graph an Equation By Plotting Points<\/div>\n<div id=\"fs-id1169596519072\" data-type=\"exercise\">\n<div id=\"fs-id1169596373126\" data-type=\"problem\">\n<p id=\"fs-id1169594153320\">Graph the equation \\(y=2x+1\\) by plotting points.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596222394\" 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-id1169596298191\" data-type=\"media\" data-alt=\"The figure shows the three step procedure for graphing a line from the equation using the example equation y equals 2x minus 1. The first step is to \u201cFind three points whose coordinates are solutions to the equation. Organize the solutions in a table\u201d. The remark is made that \u201cYou can choose any values for x or y. In this case, since y is isolated on the left side of the equation, it is easier to choose values for x\u201d. The work for the first step of the example is shown through a series of equations aligned vertically. From the top down, the equations are y equals 2x plus 1, x equals 0 (where the 0 is blue), y equals 2x plus 1, y equals 2(0) plus 1 (where the 0 is blue), y equals 0 plus 1, y equals 1, x equals 1 (where the 1 is blue), y equals 2x plus 1, y equals 2(1) plus 1 (where the 1 is blue), y equals 2 plus 1, y equals 3, x equals negative 2 (where the negative 2 is blue), y equals 2x plus 1, y equals 2(negative 2) plus 1 (where the negative 2 is blue), y equals negative 4 plus 1, y equals negative 3. The work is then organized in a table. The table has 5 rows and 3 columns. The first row is a title row with the equation y equals 2x plus 1. The second row is a header row and it labels each column. The first column header is \u201cx\u201d, the second is \u201cy\u201d and the third is \u201c(x, y)\u201d. Under the first column are the numbers 0, 1, and negative 2. Under the second column are the numbers 1, 3, and negative 3. Under the third column are the ordered pairs (0, 1), (1, 3), and (negative 2, negative 3).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_044a_img_new.jpg\" alt=\"The figure shows the three step procedure for graphing a line from the equation using the example equation y equals 2x minus 1. The first step is to \u201cFind three points whose coordinates are solutions to the equation. Organize the solutions in a table\u201d. The remark is made that \u201cYou can choose any values for x or y. In this case, since y is isolated on the left side of the equation, it is easier to choose values for x\u201d. The work for the first step of the example is shown through a series of equations aligned vertically. From the top down, the equations are y equals 2x plus 1, x equals 0 (where the 0 is blue), y equals 2x plus 1, y equals 2(0) plus 1 (where the 0 is blue), y equals 0 plus 1, y equals 1, x equals 1 (where the 1 is blue), y equals 2x plus 1, y equals 2(1) plus 1 (where the 1 is blue), y equals 2 plus 1, y equals 3, x equals negative 2 (where the negative 2 is blue), y equals 2x plus 1, y equals 2(negative 2) plus 1 (where the negative 2 is blue), y equals negative 4 plus 1, y equals negative 3. The work is then organized in a table. The table has 5 rows and 3 columns. The first row is a title row with the equation y equals 2x plus 1. The second row is a header row and it labels each column. The first column header is \u201cx\u201d, the second is \u201cy\u201d and the third is \u201c(x, y)\u201d. Under the first column are the numbers 0, 1, and negative 2. Under the second column are the numbers 1, 3, and negative 3. Under the third column are the ordered pairs (0, 1), (1, 3), and (negative 2, negative 3).\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596685141\" data-type=\"media\" data-alt=\"The second step is to \u201cPlot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work!\u201d For the example the points are (0, 1), (1, 3), and (negative 2, negative 3). A graph shows the three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points at (0, 1), (1, 3), and (negative 2, negative 3). The question \u201cDo the points line up?\u201d is stated and followed with the answer \u201cYes, the points line up.\u201d\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_044b_img_new.jpg\" alt=\"The second step is to \u201cPlot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work!\u201d For the example the points are (0, 1), (1, 3), and (negative 2, negative 3). A graph shows the three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points at (0, 1), (1, 3), and (negative 2, negative 3). The question \u201cDo the points line up?\u201d is stated and followed with the answer \u201cYes, the points line up.\u201d\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596291701\" data-type=\"media\" data-alt=\"The third step of the procedure is \u201cDraw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.\u201d A graph shows a straight line drawn through three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points at (0, 1), (1, 3), and (negative 2, negative 3). A straight line goes through all three points. The line has arrows on both ends pointing to the edge of the figure. The line is labeled with the equation y equals 2x plus 1. The statement \u201cThis line is the graph of y equals 2x plus 1\u201d is included next to the graph.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_044c_img_new.jpg\" alt=\"The third step of the procedure is \u201cDraw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.\u201d A graph shows a straight line drawn through three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points at (0, 1), (1, 3), and (negative 2, negative 3). A straight line goes through all three points. The line has arrows on both ends pointing to the edge of the figure. The line is labeled with the equation y equals 2x plus 1. The statement \u201cThis line is the graph of y equals 2x plus 1\u201d is included next to the graph.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596443288\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596764471\" data-type=\"exercise\">\n<div id=\"fs-id1169594155415\" data-type=\"problem\">\n<p id=\"fs-id1169596531818\">Graph the equation by plotting points: \\(y=2x-3\\).<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596232896\" data-type=\"solution\"><span id=\"fs-id1169596438179\" data-type=\"media\" data-alt=\"The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 2, negative 7), (negative 1, negative 5), (0, negative 3), (1, negative 1), (2, 1), (3, 3), (4, 5), and (5, 7). There are arrows at the ends of the line pointing to the outside of the figure.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_023_img_new.jpg\" alt=\"Graph of the equation y = 2x\u22123.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596316200\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594076642\" data-type=\"exercise\">\n<div id=\"fs-id1169596534537\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Graph a linear equation by plotting points.<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596453724\">The steps to take when graphing a linear equation by plotting points are summarized below.<\/p>\n\n<div id=\"fs-id1169596686979\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\"><\/div>\n<ol id=\"fs-id1169596686441\" class=\"stepwise\" type=\"1\">\n \t<li>Find three points whose coordinates are solutions to the equation. Organize them in a table.<\/li>\n \t<li>Plot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work.<\/li>\n \t<li>Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596338664\">It is true that it only takes two points to determine a line, but it is a good habit to use three points. If you only plot two points and one of them is incorrect, you can still draw a line but it will not represent the solutions to the equation. It will be the wrong line.<\/p>\n<p id=\"fs-id1169594031834\">If you use three points, and one is incorrect, the points will not line up. This tells you something is wrong and you need to check your work. Look at the difference between part (a) and part (b) in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_010\">(Figure 4)<\/a>.<\/p>\n\n<div id=\"CNX_ElemAlg_Figure_04_02_010\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"403\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_010_img_new.jpg\" alt=\"Figure a shows three points with a straight line through them. Figure b shows three points that do not lie on the same line.\" width=\"403\" height=\"165\" data-media-type=\"image\/jpeg\"> Figure .4[\/caption]\n\n<\/div>\n<p id=\"fs-id1169596410945\">Let\u2019s do another example. This time, we\u2019ll show the last two steps all on one grid.<\/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\nGraph the equation \\(y=-3x\\).\n<div id=\"fs-id1169596340938\" data-type=\"solution\">\n<div data-type=\"title\">Solution<\/div>\n<p id=\"fs-id1169596369626\">Find three points that are solutions to the equation. Here, again, it\u2019s easier to choose values for \\(x\\). Do you see why?<span data-type=\"newline\">\n<\/span><\/p>\n<span id=\"fs-id1169594239630\" data-type=\"media\" data-alt=\"The figure shows three sets of equations used to determine ordered pairs from the equation y equals negative 3x. The first set has the equations: x equals 0 (where the 0 is blue), y equals negative 3x, y equals negative 3(0) (where the 0 is blue), y equals 0. The second set has the equations: x equals 1 (where the 1 is blue), y equals negative 3x, y equals negative 3(1) (where the 1 is blue), y equals negative 3. The third set has the equations: x equals negative 2 (where the negative 2 is blue), y equals negative 3x, y equals negative 3(negative 2) (where the negative 2 is blue), y equals 6.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_025_img_new.jpg\" alt=\"The figure shows three sets of equations used to determine ordered pairs from the equation y equals negative 3x. The first set has the equations: x equals 0 (where the 0 is blue), y equals negative 3x, y equals negative 3(0) (where the 0 is blue), y equals 0. The second set has the equations: x equals 1 (where the 1 is blue), y equals negative 3x, y equals negative 3(1) (where the 1 is blue), y equals negative 3. The third set has the equations: x equals negative 2 (where the negative 2 is blue), y equals negative 3x, y equals negative 3(negative 2) (where the negative 2 is blue), y equals 6.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596518462\">We list the points in the table below.<span data-type=\"newline\">\n<\/span><\/p>\n\n<table id=\"fs-id1169596654135\" class=\"grid\" style=\"width: 100%;\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation y equals negative 3x. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 1, and negative 2. Under the second column are the numbers 0, negative 3, and 6. Under the third column are the ordered pairs (0, 0), (1, negative 3), and (negative 2, 6).\"><caption>\\(y=-3x\\)<\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(0,0\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(-3\\)<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(1,-3\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">\\(-2\\)<\/td>\n<td data-valign=\"middle\" data-align=\"center\">6<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(-2,6\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596275520\">Plot the points, check that they line up, and draw the line.<span data-type=\"newline\">\n<\/span><\/p>\n<span id=\"fs-id1169596310903\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn through three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points which are labeled by their ordered pairs (negative 2, 6), (0, 0), and (1, negative 3). A straight line goes through all three points. The line has arrows on both ends pointing to the outside of the figure. The line is labeled with the equation y equals negative 3x.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_011_img_new.jpg\" alt=\"Graph of the equation y = \u22123x. The points listed in the previous table are plotted.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596656657\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594157527\" data-type=\"exercise\">\n<div id=\"fs-id1169594159171\" data-type=\"problem\">\n<p id=\"fs-id1169594150201\">Graph the equation by plotting points: \\(y=-4x\\).<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169594085758\" data-type=\"solution\"><span id=\"fs-id1169596704588\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 2, 8), (0, 0), and (2, negative 8). The line has arrows on both ends pointing to the outside of the figure.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_012_img_new.jpg\" alt=\"A graph of the equation y = \u22124x.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\">\n\nWhen an equation includes a fraction as the coefficient of \\(x\\), we can still substitute any numbers for \\(x\\). But the math is easier if we make \u2018good\u2019 choices for the values of \\(x\\). This way we will avoid fraction answers, which are hard to graph precisely.\n\n<\/div>\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-id1169596362679\" data-type=\"problem\">\n<p id=\"fs-id1169596702145\">Graph the equation \\(y=\\dfrac{1}{2}x+3\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594002064\" 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-id1169596299233\">Find three points that are solutions to the equation. Since this equation has the fraction \\(\\dfrac{1}{2}\\) as a coefficient of \\(x,\\) we will choose values of \\(x\\) carefully. We will use zero as one choice and multiples of 2 for the other choices. Why are multiples of 2 a good choice for values of \\(x\\)?<span data-type=\"newline\">\n<\/span><\/p>\n<span id=\"fs-id1169596440466\" data-type=\"media\" data-alt=\"The figure shows three sets of equations used to determine ordered pairs from the equation y equals (one half)x plus 3. The first set has the equations: x equals 0 (where the 0 is blue), y equals (one half)x plus 3, y equals (one half)(0) plus 3 (where the 0 is blue), y equals 0 plus 3, y equals 3. The second set has the equations: x equals 2 (where the 2 is blue), y equals (one half)x plus 3, y equals (one half)(2) plus 3 (where the 2 is blue), y equals 1 plus 3, y equals 4. The third set has the equations: x equals 4 (where the 4 is blue), y equals (one half)x plus 3, y equals (one half)(4) plus 3 (where the 4 is blue), y equals 2 plus 3, y equals 5.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_026_img_new.jpg\" alt=\"The figure shows three sets of equations used to determine ordered pairs from the equation y equals (one half)x plus 3. The first set has the equations: x equals 0 (where the 0 is blue), y equals (one half)x plus 3, y equals (one half)(0) plus 3 (where the 0 is blue), y equals 0 plus 3, y equals 3. The second set has the equations: x equals 2 (where the 2 is blue), y equals (one half)x plus 3, y equals (one half)(2) plus 3 (where the 2 is blue), y equals 1 plus 3, y equals 4. The third set has the equations: x equals 4 (where the 4 is blue), y equals (one half)x plus 3, y equals (one half)(4) plus 3 (where the 4 is blue), y equals 2 plus 3, y equals 5.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169594086177\">The points are shown in the table below.<\/p>\n\n<table id=\"fs-id1169596641191\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation y equals (one half)x plus 3. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 2, and 4. Under the second column are the numbers 3, 4, and 5. Under the third column are the ordered pairs (0, 3), (2, 4), and (4, 5).\"><caption><strong data-effect=\"bold\">\\(y=\\dfrac{1}{2}x+3\\)<\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(0,3\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(2,4\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">5<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(4,5\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594156783\">Plot the points, check that they line up, and draw the line.<span data-type=\"newline\">\n<\/span><\/p>\n<span id=\"fs-id1169594189788\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn through three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points which are labeled by their ordered pairs (0, 3), (2, 4), and (4, 5). A straight line goes through all three points. The line has arrows on both ends pointing to the outside of the figure. The line is labeled with the equation y equals (one half)x plus 3.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_014_img_new.jpg\" alt=\"The points listed in the previous table are plotted. The equation y = 1 half x + 3 is graphed.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596392359\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596392362\" data-type=\"exercise\">\n<div id=\"fs-id1169596392364\" data-type=\"problem\">\n<p id=\"fs-id1169594004706\">Graph the equation \\(y=\\dfrac{1}{3}x-1\\).<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596565866\" data-type=\"solution\"><span id=\"fs-id1169596439026\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 9, negative 4), (negative 6, negative 3), (negative 3, negative 2), (0, negative 1), (3, 0), (6, 1), and (9, 2). The line has arrows on both ends pointing to the outside of the figure.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_015_img_new.jpg\" alt=\"A graph of the equation y = 1 third x\u22121.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596686309\">So far, all the equations we graphed had \\(y\\) given in terms of \\(x\\). Now we\u2019ll graph an equation with \\(x\\) and \\(y\\) on the same side. Let\u2019s see what happens in the equation \\(2x+y=3\\). If \\(y=0\\) what is the value of \\(x\\)?<\/p>\n<span id=\"fs-id1169596445877\" data-type=\"media\" data-alt=\"The figure shows a set of equations used to determine an ordered pair from the equation 2x plus y equals 3. The first equation is y equals 0 (where the 0 is red). The second equation is the two- variable equation 2x plus y equals 3. The third equation is the onenegative variable equation 2x plus 0 equals 3 (where the 0 is red). The fourth equation is 2x equals 3. The fifth equation is x equals three halves. The last line is the ordered pair (three halves, 0).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_027_img_new.jpg\" alt=\"The figure shows a set of equations used to determine an ordered pair from the equation 2x plus y equals 3. The first equation is y equals 0 (where the 0 is red). The second equation is the two- variable equation 2x plus y equals 3. The third equation is the onenegative variable equation 2x plus 0 equals 3 (where the 0 is red). The fourth equation is 2x equals 3. The fifth equation is x equals three halves. The last line is the ordered pair (three halves, 0).\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596445921\">This point has a fraction for the <em data-effect=\"italics\">x<\/em>- coordinate and, while we could graph this point, it is hard to be precise graphing fractions. Remember in the example \\(y=\\dfrac{1}{2}x+3\\), we carefully chose values for \\(x\\) so as not to graph fractions at all. If we solve the equation \\(2x+y=3\\) for \\(y\\), it will be easier to find three solutions to the equation.<\/p>\n\\(\\begin{array}{ccc}\\hfill 2x+y&amp; =\\hfill &amp; 3\\hfill \\\\ \\hfill y&amp; =\\hfill &amp; -2x+3\\hfill \\end{array}\\)\n<p id=\"fs-id1169596382780\">The solutions for \\(x=0\\), \\(x=1\\), and \\(x=-1\\) are shown in the table below. The graph is shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_017\">(Figure 5)<\/a>.<\/p>\n\n<table id=\"fs-id1169596387360\" class=\"aligncenter\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation 2x plus y equals 3. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 1, and negative 1. Under the second column are the numbers 3, 1, and 5. Under the third column are the ordered pairs (0, 3), (1, 1), and (negative 1, 5).\"><caption><strong data-effect=\"bold\">\\(2x+y=3\\)<\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(0,3\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(1,1\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">\\(-1\\)<\/td>\n<td data-valign=\"middle\" data-align=\"center\">5<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(-1,5\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"CNX_ElemAlg_Figure_04_02_017\" class=\"bc-figure figure\">\n\n&nbsp;\n\n[caption id=\"\" align=\"aligncenter\" width=\"362\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_017_img_new.jpg\" alt=\"The points listed in the previous table are plotted. The equation 2x + y = 3 is graphed.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\"> Figure .5[\/caption]\n\n<\/div>\n<p id=\"fs-id1169596376662\">Can you locate the point \\(\\left(\\dfrac{3}{2},0\\right)\\), which we found by letting \\(y=0\\), on the line?<\/p>\n\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-id1169594029163\" data-type=\"problem\">\n<p id=\"fs-id1169594029165\">Graph the equation \\(3x+y=-1\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596754513\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-846\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td>Find three points that are solutions to the equation.<\/td>\n<td>\\(3x+y\\phantom{\\rule{0.5em}{0ex}}=\\phantom{\\rule{0.5em}{0ex}}-1\\)<\/td>\n<\/tr>\n<tr>\n<td>First, solve the equation for \\(y\\).<\/td>\n<td>\\(y\\phantom{\\rule{0.5em}{0ex}}=\\phantom{\\rule{0.5em}{0ex}}-3x-1\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596364491\">We\u2019ll let \\(x\\) be 0, 1, and \\(-1\\) to find 3 points. The ordered pairs are shown in the table below. Plot the points, check that they line up, and draw the line. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_018\">(Figure 6)<\/a>.<\/p>\n\n<table id=\"fs-id1169596364512\" class=\"aligncenter\" style=\"height: 70px; width: 100%;\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation 3x plus y equals negative 1. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 1, and negative 1. Under the second column are the numbers negative 1, negative 4, and 2. Under the third column are the ordered pairs (0, negative 1), (1, negative 4), and (negative 1, 2).\"><caption><strong data-effect=\"bold\">\\(3x+y=-1\\)<\/strong><\/caption>\n<tbody>\n<tr style=\"height: 14px;\" valign=\"top\">\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"height: 14px; width: 238.406px;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\" valign=\"top\">\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"middle\" data-align=\"center\">\\(-1\\)<\/td>\n<td style=\"height: 14px; width: 238.406px;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(0,-1\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\" valign=\"top\">\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"middle\" data-align=\"center\">\\(-4\\)<\/td>\n<td style=\"height: 14px; width: 238.406px;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(1,-4\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\" valign=\"top\">\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"middle\" data-align=\"center\">\\(-1\\)<\/td>\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td style=\"height: 14px; width: 238.406px;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(-1,2\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"CNX_ElemAlg_Figure_04_02_018\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"360\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_018_img_new.jpg\" alt=\"The points listed in the previous table are plotted. The equation 3x+y = \u22121 is graphed.\" width=\"360\" height=\"367\" data-media-type=\"image\/jpeg\"> Figure .6[\/caption]\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596314007\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596314011\" data-type=\"exercise\">\n<div id=\"fs-id1169596314014\" data-type=\"problem\">\n<p id=\"fs-id1169596314016\">Graph the equation \\(2x+y=2\\).<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596314036\" data-type=\"solution\"><span id=\"fs-id1169596314039\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, 10), (negative 2, 6), (0, 2), (2, negative 2), (4, negative 6), and (6, negative 10). The line has arrows on both ends pointing to the outside of the figure.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_019_img_new.jpg\" alt=\"Graph of the equation 2 x + y = 2.\" width=\"243\" height=\"249\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\"><\/div>\n<\/div>\n<p id=\"fs-id1169596446914\">If you can choose any three points to graph a line, how will you know if your graph matches the one shown in the answers in the book? If the points where the graphs cross the <em data-effect=\"italics\">x<\/em>- and <em data-effect=\"italics\">y<\/em>-axis are the same, the graphs match!<\/p>\n<p id=\"fs-id1169596446930\">The equation in <a class=\"autogenerated-content\" href=\"#fs-id1169596376662\">(Example 5)<\/a> was written in standard form, with both \\(x\\) and \\(y\\) on the same side. We solved that equation for \\(y\\) in just one step. But for other equations in standard form it is not that easy to solve for \\(y\\), so we will leave them in standard form. We can still find a first point to plot by letting \\(x=0\\) and solving for \\(y\\). We can plot a second point by letting \\(y=0\\) and then solving for \\(x\\). Then we will plot a third point by using some other value for \\(x\\) or \\(y\\).<\/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 id=\"fs-id1169596438837\" data-type=\"problem\">\n<p id=\"fs-id1169594030848\">Graph the equation \\(2x-3y=6\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594030870\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-511\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td>Find three points that are solutions to the equation.<\/td>\n<td>\\(\\begin{array}{ccc}\\hfill 2x-3y&amp; =\\hfill &amp; 6\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>First, let \\(x=0\\).<\/td>\n<td>\\(\\begin{array}{ccc}\\hfill 2\\left(0\\right)-3y&amp; =\\hfill &amp; 6\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>Solve for \\(y\\).<\/td>\n<td>\\(\\begin{array}{ccc}\\hfill -3y&amp; =\\hfill &amp; 6\\hfill \\\\ \\hfill y&amp; =\\hfill &amp; -2\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>Now let \\(y=0\\).<\/td>\n<td>\\(\\begin{array}{ccc}\\hfill 2x-3\\left(0\\right)&amp; =\\hfill &amp; 6\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>Solve for \\(x\\).<\/td>\n<td>\\(\\begin{array}{ccc}\\hfill 2x&amp; =\\hfill &amp; 6\\hfill \\\\ \\hfill x&amp; =\\hfill &amp; 3\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>We need a third point. Remember, we can choose any value for \\(x\\) or \\(y\\). We'll let \\(x=6\\).<\/td>\n<td>\\(\\begin{array}{ccc}\\hfill 2\\left(6\\right)-3y&amp; =\\hfill &amp; 6\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>Solve for \\(y\\).<\/td>\n<td>\\(\\begin{array}{ccc}\\hfill 12-3y&amp; =\\hfill &amp; 6\\hfill \\\\ \\hfill -3y&amp; =\\hfill &amp; -6\\hfill \\\\ \\hfill y&amp; =\\hfill &amp; 2\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596548028\">We list the ordered pairs in the table below. Plot the points, check that they line up, and draw the line. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_029\">(Figure 7)<\/a>.<\/p>\n\n<table id=\"fs-id1169596548039\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation 2x negative 3y equals 6. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 3, and 6. Under the second column are the numbers negative 2, 0, and 2. Under the third column are the ordered pairs (0, negative 2), (3, 0), and (6, 2).\"><caption><strong data-effect=\"bold\">\\(2x-3y=6\\)<\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(-2\\)<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(0,-2\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(3,0\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">6<\/td>\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(6,2\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"CNX_ElemAlg_Figure_04_02_029\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"362\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_029_img_new.jpg\" alt=\"The points listed in previous table are plotted. The equation 2x \u2212 3y = 6 is plotted.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\"> Figure .7[\/caption]\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<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596381106\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596381110\" data-type=\"exercise\">\n<div id=\"fs-id1169596381112\" data-type=\"problem\">\n<p id=\"fs-id1169596381114\">Graph the equation \\(4x+2y=8\\).<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596381137\" data-type=\"solution\"><span id=\"fs-id1169596381140\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 1, 6), (0, 4), (1, 2), (2, 0), (3, negative 2), and (4, negative 4). The line has arrows on both ends pointing to the outside of the figure.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_030_img_new.jpg\" alt=\"Graph of the equation 4x + 2y = 8.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<div id=\"fs-id1169596381158\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596381162\" data-type=\"exercise\">\n<div id=\"fs-id1169596387128\" data-type=\"solution\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Graph Vertical and Horizontal Lines<\/h1>\n<p id=\"fs-id1169596387156\">Can we graph an equation with only one variable? Just \\(x\\) and no \\(y\\), or just \\(y\\) without an \\(x\\)? How will we make a table of values to get the points to plot?<\/p>\n<p id=\"fs-id1169594240483\">Let\u2019s consider the equation \\(x=-3\\). This equation has only one variable, \\(x\\). The equation says that \\(x\\) is <em data-effect=\"italics\">always<\/em> equal to \\(-3\\), so its value does not depend on \\(y\\). No matter what \\(y\\) is, the value of \\(x\\) is always \\(-3\\).<\/p>\n<p id=\"fs-id1169596226049\">So to make a table of values, write \\(-3\\) in for all the \\(x\\) values. Then choose any values for \\(y\\). Since \\(x\\) does not depend on \\(y\\), you can choose any numbers you like. But to fit the points on our coordinate graph, we\u2019ll use 1, 2, and 3 for the <em data-effect=\"italics\">y<\/em>-coordinates. See the table below.<\/p>\n\n<table id=\"fs-id1169596226086\" class=\"aligncenter\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation x equals negative 3. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers negative 3, negative 3, and negative 3. Under the second column are the numbers 1, 2, and 3. Under the third column are the ordered pairs (negative 3, 1), (negative 3, 2), and (negative 3, 3).\"><caption><strong data-effect=\"bold\">\\(x=-3\\)<\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">\\(-3\\)<\/td>\n<td data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(-3,1\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">\\(-3\\)<\/td>\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(-3,2\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">\\(-3\\)<\/td>\n<td data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(-3,3\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594079050\">Plot the points from the table and connect them with a straight line. Notice in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_032\">(Figure 8)<\/a> that we have graphed a <em data-effect=\"italics\">vertical line<\/em>.<\/p>\n\n<div id=\"CNX_ElemAlg_Figure_04_02_032\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"362\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_032_img_new.jpg\" alt=\"The points listed in the previous table are plotted. The equation x = \u22123 is graphed. The resulting line is vertical.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\"> Figure .8[\/caption]\n\n<\/div>\n<div id=\"fs-id1169594079091\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Vertical line<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169594178158\">A <span data-type=\"term\">vertical line<\/span> is the graph of an equation of the form \\(x=a\\).<\/p>\n<p id=\"fs-id1169594178174\">The line passes through the <em data-effect=\"italics\">x<\/em>-axis at \\(\\left(a,0\\right)\\).<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"title\">\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-id1169594178204\" data-type=\"problem\">\n<p id=\"fs-id1169594178206\">Graph the equation \\(x=2\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594150626\" 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-id1169594150632\">The equation has only one variable, \\(x\\), and \\(x\\) is always equal to 2. We create the table below where \\(x\\) is always 2 and then put in any values for \\(y\\). The graph is a vertical line passing through the <em data-effect=\"italics\">x<\/em>-axis at 2. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_033\">(Figure 9)<\/a>.<\/p>\n\n<table id=\"fs-id1169594150665\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation x equals 2. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 2, 2, and 2. Under the second column are the numbers 1, 2, and 3. Under the third column are the ordered pairs (2, 1), (2, 2), and (2, 3).\"><caption><strong data-effect=\"bold\">\\(x=2\\)<\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(2,1\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(2,2\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(2,3\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"CNX_ElemAlg_Figure_04_02_033\" class=\"bc-figure figure\" style=\"text-align: center;\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"362\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_033_img_new.jpg\" alt=\"The points listed in the previous table are plotted. The equation x = 2 is graphed. The resulting line is vertical.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\"> Figure .9[\/caption]\n\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 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594129269\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594129273\" data-type=\"exercise\">\n<div id=\"fs-id1169594129275\" data-type=\"problem\">\n<p id=\"fs-id1169594129277\">Graph the equation \\(x=5\\).<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169594129291\" data-type=\"solution\"><span id=\"fs-id1169594129294\" data-type=\"media\" data-alt=\"The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (5, 1), (5, 2), (5, 3), and all other points with first coordinate 5. The line has arrows on both ends pointing to the outside of the figure.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_034_img_new.jpg\" alt=\"Graph of the equation x = 5. The resulting line is vertical.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\">\n\nWhat if the equation has \\(y\\) but no \\(x\\)? Let\u2019s graph the equation \\(y=4\\). This time the <em>y<\/em>- value is a constant, so in this equation, \\(y\\) does not depend on \\(x\\). Fill in 4 for all the \\(y\\)\u2019s in the table below and then choose any values for \\(x\\). We\u2019ll use 0, 2, and 4 for the <em>x<\/em>-coordinates.\n\n<\/div>\n<\/div>\n<table id=\"fs-id1169594030456\" class=\"aligncenter\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation y equals 4. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 2, and 4. Under the second column are the numbers 4, 4, and 4. Under the third column are the ordered pairs (0, 4), (2, 4), and (4, 4).\"><caption><strong data-effect=\"bold\">\\(y=4\\)<\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(0,4\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(2,4\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(4,4\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596754204\">The graph is a horizontal line passing through the <em data-effect=\"italics\">y<\/em>-axis at 4. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_036\">(Figure 10)<\/a>.<\/p>\n\n<div id=\"CNX_ElemAlg_Figure_04_02_036\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"362\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_036_img_new.jpg\" alt=\"The points listed in the previous table are plotted. The equation y = 4 is graphed. The resulting line is horizontal.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\"> Figure .10[\/caption]\n\n<\/div>\n<div id=\"fs-id1169596409604\" data-type=\"note\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Horizontal line<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596409609\">A <span data-type=\"term\">horizontal line<\/span> is the graph of an equation of the form \\(y=b\\).<\/p>\n<p id=\"fs-id1169596409625\">The line passes through the <em data-effect=\"italics\">y<\/em>-axis at \\(\\left(0,b\\right)\\).<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596409655\" data-type=\"problem\">\n<p id=\"fs-id1169596409657\">Graph the equation \\(y=-1.\\)<\/p>\n\n<\/div>\n<div 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-id1169596652714\">The equation \\(y=-1\\) has only one variable, \\(y\\). The value of \\(y\\) is constant. All the ordered pairs in the table below have the same <em data-effect=\"italics\">y<\/em>-coordinate. The graph is a horizontal line passing through the <em data-effect=\"italics\">y<\/em>-axis at \\(-1\\), as shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_037\">(Figure 11)<\/a>.<\/p>\n\n<table style=\"width: 100%;\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation y equals negative 1. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 3, and negative 3. Under the second column are the numbers negative 1, negative 1, and negative 1. Under the third column are the ordered pairs (0, negative 1), (3, negative 1), and (negative 3, negative 1).\"><caption><strong data-effect=\"bold\">\\(y=-1\\)<\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(-1\\)<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(0,-1\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(-1\\)<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(3,-1\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">\\(-3\\)<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(-1\\)<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(-3,-1\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"CNX_ElemAlg_Figure_04_02_037\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"362\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_037_img_new.jpg\" alt=\"The points listed in the previous table are plotted. The equation y = \u22121 is graphed. The resulting line is horizontal.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\"> Figure .11[\/caption]\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 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594008580\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594008584\" data-type=\"exercise\">\n<div id=\"fs-id1169594008586\" data-type=\"problem\">\n<p id=\"fs-id1169594008588\">Graph the equation \\(y=-4\\).<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169594008602\" data-type=\"solution\"><span id=\"fs-id1169594008605\" data-type=\"media\" data-alt=\"The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, negative 4), (0, negative 4), (4, negative 4), and all other points with second coordinate negative 4. The line has arrows on both ends pointing to the outside of the figure.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_038_img_new.jpg\" alt=\"Graph of the equation y = \u22124. The resulting line is horizontal.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\">\n\nThe equations for vertical and horizontal lines look very similar to equations like \\(y=4x.\\) What is the difference between the equations \\(y=4x\\) and \\(y=4\\)?\n\n<\/div>\n<\/div>\n<p id=\"fs-id1169594123637\">The equation \\(y=4x\\) has both \\(x\\) and \\(y\\). The value of \\(y\\) depends on the value of \\(x\\). The <em data-effect=\"italics\">y<\/em>-coordinate changes according to the value of \\(x\\). The equation \\(y=4\\) has only one variable. The value of \\(y\\) is constant. The <em data-effect=\"italics\">y<\/em>-coordinate is always 4. It does not depend on the value of \\(x\\). See the tables below.<\/p>\n\n<table id=\"fs-id1169594030456\" class=\"aligncenter\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation y equals 4. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 2, and 4. Under the second column are the numbers 4, 4, and 4. Under the third column are the ordered pairs (0, 4), (2, 4), and (4, 4).\"><caption><strong data-effect=\"bold\">\\(y=4x\\)<\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(0,4\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(2,4\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(4,4\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div>\n<table id=\"fs-id1169594030456\" class=\"aligncenter\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation y equals 4. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 2, and 4. Under the second column are the numbers 4, 4, and 4. Under the third column are the ordered pairs (0, 4), (2, 4), and (4, 4).\"><caption><strong data-effect=\"bold\">\\(y=4\\)<\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(0,0\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(1,4\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">8<\/td>\n<td data-valign=\"middle\" data-align=\"center\">\\(\\left(2,8\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"CNX_ElemAlg_Figure_04_02_040\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"362\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_040_img_new.jpg\" alt=\"The equations y = 4 and y = 4x are graphed and labelled.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\"> Figure .12[\/caption]\n\n<\/div>\n<p id=\"fs-id1169594034174\">Notice, in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_040\">(Figure 12)<\/a>, the equation \\(y=4x\\) gives a slanted line, while \\(y=4\\) gives a horizontal line.<\/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 id=\"fs-id1169596446108\" data-type=\"problem\">\n<p id=\"fs-id1169596446110\">Graph \\(y=-3x\\) and \\(y=-3\\) in the same rectangular coordinate system.<\/p>\n\n<\/div>\n<div id=\"fs-id1169596446136\" 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-id1169596446141\">Notice that the first equation has the variable \\(x\\), while the second does not. See the tables below. The two graphs are shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_041\">(Figure 13)<\/a>.<\/p>\n\n<div>\n<table id=\"fs-id1169596446157\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"There are two tables, each with 5 rows and 3 columns. For the table on the left: The first row is a title row with the equation y equals negative 3x. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 1, and 2. Under the second column are the numbers 0, negative 3, and negative 6. Under the third column are the ordered pairs (0, 0), (1, negative 3), and (2, negative 6). For the table on the right: The first row is a title row with the equation y equals negative 3. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 1, and 2. Under the second column are the numbers negative 3, negative 3, and negative 3. Under the third column are the ordered pairs (0, negative 3), (1, negative 3), and (2, negative 3).\"><caption><strong data-effect=\"bold\">\\(y=-3x\\)<\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 40px; height: 16px;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 47px; height: 16px;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 125px; height: 16px;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 40px; height: 16px;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 47px; height: 16px;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 125px; height: 16px;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(0,0\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 40px; height: 16px;\" data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td style=\"width: 47px; height: 16px;\" data-valign=\"middle\" data-align=\"center\">\\(-3\\)<\/td>\n<td style=\"width: 125px; height: 16px;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(1,-3\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 40px; height: 16px;\" data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td style=\"width: 47px; height: 16px;\" data-valign=\"middle\" data-align=\"center\">\\(-6\\)<\/td>\n<td style=\"width: 125px; height: 16px;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(2,-6\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"fs-id1169596446157\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"There are two tables, each with 5 rows and 3 columns. For the table on the left: The first row is a title row with the equation y equals negative 3x. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 1, and 2. Under the second column are the numbers 0, negative 3, and negative 6. Under the third column are the ordered pairs (0, 0), (1, negative 3), and (2, negative 6). For the table on the right: The first row is a title row with the equation y equals negative 3. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 1, and 2. Under the second column are the numbers negative 3, negative 3, and negative 3. Under the third column are the ordered pairs (0, negative 3), (1, negative 3), and (2, negative 3).\"><caption><strong data-effect=\"bold\">\\(y=-3\\)<\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 41px; height: 16px;\" data-align=\"center\" data-valign=\"top\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 46px; height: 16px;\" data-align=\"center\" data-valign=\"top\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 126px; height: 16px;\" data-align=\"center\" data-valign=\"top\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 41px; height: 16px;\" data-align=\"center\" data-valign=\"top\">0<\/td>\n<td style=\"width: 46px; height: 16px;\" data-align=\"center\" data-valign=\"top\">\\(-3\\)<\/td>\n<td style=\"width: 126px; height: 16px;\" data-align=\"center\" data-valign=\"top\">\\(\\left(0,-3\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 41px; height: 16px;\" data-align=\"center\" data-valign=\"top\">1<\/td>\n<td style=\"width: 46px; height: 16px;\" data-align=\"center\" data-valign=\"top\">\\(-3\\)<\/td>\n<td style=\"width: 126px; height: 16px;\" data-align=\"center\" data-valign=\"top\">\\(\\left(1,-3\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 41px; height: 16px;\" data-align=\"center\" data-valign=\"top\">2<\/td>\n<td style=\"width: 46px; height: 16px;\" data-align=\"center\" data-valign=\"top\">\\(-3\\)<\/td>\n<td style=\"width: 126px; height: 16px;\" data-align=\"center\" data-valign=\"top\">\\(\\left(2,-3\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"CNX_ElemAlg_Figure_04_02_041\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"362\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_041_img_new.jpg\" alt=\"The equations y = \u22123 and y = \u22123x are graphed and labelled. The equation y = \u22123x is a slanted line while y = \u22123 is horizontal.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\"> Figure .13[\/caption]\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<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596446275\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596446279\" data-type=\"exercise\">\n<div id=\"fs-id1169596446281\" data-type=\"problem\">\n<p id=\"fs-id1169596446283\">Graph \\(y=-4x\\) and \\(y=-4\\) in the same rectangular coordinate system.<\/p>\n\n<\/div>\n<details><summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596446309\" data-type=\"solution\"><span id=\"fs-id1169596446312\" data-type=\"media\" data-alt=\"The figure shows a two straight lines drawn on the same x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. One line is a straight horizontal line going through the points (negative 4, negative 4), (0, negative 4), (4, negative 4), and all other points with second coordinate negative 4. The other line is a slanted line going through the points (negative 2, 8), (negative 1, 4), (0, 0), (1, negative 4), and (2, negative 8).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_042_img_new.jpg\" alt=\"The equations y = \u22124 and y = \u22124x are graphed and labelled. The equation y = \u22124x is a slanted line while y = \u22124 is horizontal.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"fs-id1169594154430\" data-bullet-style=\"bullet\">\n \t<li><strong data-effect=\"bold\">Graph a Linear Equation by Plotting Points<\/strong>\n<ol id=\"fs-id1169594079036\" class=\"stepwise\" type=\"1\">\n \t<li>Find three points whose coordinates are solutions to the equation. Organize them in a table.<\/li>\n \t<li>Plot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work!<\/li>\n \t<li>Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1 data-type=\"title\">Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1169594176658\">\n \t<dt>graph of a linear equation<\/dt>\n \t<dd id=\"fs-id1169594176664\">The graph of a linear equation \\(Ax+By=C\\) is a straight line. Every point on the line is a solution of the equation. Every solution of this equation is a point on this line.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594176687\">\n \t<dt>horizontal line<\/dt>\n \t<dd id=\"fs-id1169594176692\">A horizontal line is the graph of an equation of the form \\(y=b\\). The line passes through the <em data-effect=\"italics\">y<\/em>-axis at \\(\\left(0,b\\right)\\).<\/dd>\n<\/dl>\n<dl id=\"fs-id1169596554286\">\n \t<dt>vertical line<\/dt>\n \t<dd id=\"fs-id1169596554292\">A vertical line is the graph of an equation of the form \\(x=a\\). The line passes through the <em data-effect=\"italics\">x<\/em>-axis at \\(\\left(a,0\\right)\\).<\/dd>\n<\/dl>\n<\/div>\n<h1 data-type=\"title\">3.2 Exercise Set<\/h1>\n<p id=\"fs-id1169594212944\">In the following exercises, for each ordered pair, decide:<\/p>\n<span class=\"token\">a)<\/span> Is the ordered pair a solution to the equation?\u2003b) Is the point on the line?\n<ol>\n \t<li>\\(y=x+2\\)\n<ol type=\"A\">\n \t<li>\\(\\left(0,2\\right)\\)<\/li>\n \t<li>\\(\\left(1,2\\right)\\)<\/li>\n \t<li>\\(\\left(-1,1\\right)\\)<\/li>\n \t<li>\\(\\left(-3,-1\\right)\\)<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<table class=\" aligncenter\" style=\"border-collapse: collapse; width: 45.0873%; height: 278px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 100%;\"><span id=\"fs-id1169594008347\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, negative 4), (negative 5, negative 3), (negative 4, negative 2), (negative 3, negative 1), (negative 2, 0), (negative 1, 1), (0, 2), (1, 3), (2, 4), (3, 5), (4, 6), and (5, 7).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_259_img_new.jpg\" alt=\"Graph of the equation y = x + 2.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol start=\"2\">\n \t<li>\\(y=\\dfrac{1}{2}x-3\\)\n<ol type=\"A\">\n \t<li>\\(\\left(0,-3\\right)\\)<\/li>\n \t<li>\\(\\left(2,-2\\right)\\)<\/li>\n \t<li>\\(\\left(-2,-4\\right)\\)<\/li>\n \t<li>\\(\\left(4,1\\right)\\)<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<table class=\" aligncenter\" style=\"border-collapse: collapse; width: 28.3843%; height: 30px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 100%;\"><span data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, negative 6), (negative 4, negative 5), (negative 2, negative 4), (0, negative 3), (2, negative 2), (4, negative 1), and (6, 0).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_261_img_new.jpg\" alt=\"Graph of the equation y = 1 half x \u2212 3.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596319037\">In the following exercises, graph by plotting points.<\/p>\n\n<ol class=\"twocolumn\" start=\"3\">\n \t<li>\\(y=3x-1\\)<\/li>\n \t<li>\\(y=-3x+3\\)<\/li>\n \t<li>\\(y=x+2\\)<\/li>\n \t<li>\\(y=-x-3\\)<\/li>\n \t<li>\\(y=2x\\)<\/li>\n \t<li>\\(y=3x\\)<\/li>\n \t<li>\\(y=\\dfrac{1}{2}x+2\\)<\/li>\n \t<li>\\(y=\\dfrac{4}{3}x-5\\)<\/li>\n \t<li>\\(y=-\\dfrac{2}{5}x+1\\)<\/li>\n \t<li>\\(y=-\\dfrac{3}{2}x+2\\)<\/li>\n \t<li>\\(x+y=6\\)<\/li>\n \t<li>\\(x+y=-3\\)<\/li>\n \t<li>\\(x-y=2\\)<\/li>\n \t<li>\\(x-y=-1\\)<\/li>\n \t<li>\\(3x+y=7\\)<\/li>\n \t<li>\\(2x+y=-3\\)<\/li>\n \t<li>\\(\\dfrac{1}{3}x+y=2\\)<\/li>\n \t<li>\\(-\\dfrac{1}{2}x-y=-3\\)<\/li>\n \t<li>\\(2x+3y=12\\)<\/li>\n \t<li>\\(3x-4y=12\\)<\/li>\n \t<li>\\(x-6y=3\\)<\/li>\n \t<li>\\(3x+y=2\\)<\/li>\n<\/ol>\n<p id=\"fs-id1169596686274\">In the following exercises, graph each equation.<\/p>\n\n<ol class=\"twocolumn\" start=\"25\">\n \t<li>\\(x=4\\)<\/li>\n \t<li>\\(x=-2\\)<\/li>\n \t<li>\\(y=3\\)<\/li>\n \t<li>\\(y=-5\\)<\/li>\n \t<li>\\(x=\\dfrac{7}{3}\\)<\/li>\n \t<li>\\(y=-\\dfrac{15}{4}\\)<\/li>\n<\/ol>\n<p id=\"fs-id1169596635837\">In the following exercises, graph each pair of equations in the same rectangular coordinate system.<\/p>\n\n<ol class=\"twocolumn\" start=\"31\">\n \t<li>\\(y=2x\\) and \\(y=2\\)<\/li>\n \t<li>\\(y=-\\dfrac{1}{2}x\\) and \\(y=-\\dfrac{1}{2}\\)<\/li>\n<\/ol>\n<ol start=\"33\">\n \t<li>The Stonechilds rented a motor home for one week to go on vacation. It cost them \\$594 plus \\$0.32 per mile to rent the motor home, so the linear equation \\(y=594+0.32x\\) gives the cost, \\(y\\), for driving \\(x\\) miles. Calculate the rental cost for driving 400, 800, and 1200 miles, and then graph the line.<\/li>\n<\/ol>\n<h1>Answers<\/h1>\n<ol class=\"twocolumn\">\n \t<li>\n<ol type=\"A\">\n \t<li>yes; no<\/li>\n \t<li>no; no<\/li>\n \t<li>yes; yes<\/li>\n \t<li>yes; yes<\/li>\n<\/ol>\n<\/li>\n \t<li>\n<ol type=\"A\">\n \t<li>yes; yes<\/li>\n \t<li>yes; yes<\/li>\n \t<li>yes; yes<\/li>\n \t<li>no; no<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<table style=\"border-collapse: collapse; width: 100%; height: 802px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 337px;\">\n<td style=\"height: 337px; width: 50.2516%;\">3.\n\n<span id=\"fs-id1169594030487\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, negative 10), (negative 2, negative 7), (negative 1, negative 4), (0, negative 1), (1, 2), (2, 5), and (3, 8).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_201_img_new.jpg\" alt=\"Graph of the equation y = 3x \u2212 1.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span>\n\n&nbsp;<\/td>\n<td style=\"height: 337px; width: 49.7484%;\">4.\n\n<img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_203_img_new.jpg\" alt=\"Graph of the equation y = \u22123x + 3.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/td>\n<\/tr>\n<tr style=\"height: 336px;\">\n<td style=\"height: 336px; width: 50.2516%;\">5.\n\n<span id=\"fs-id1169594073542\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 10, negative 8), (negative 9, negative 7), (negative 8, negative 6), (negative 7, negative 5), (negative 6, negative 4), (negative 5, negative 3), (negative 4, negative 2), (negative 3, negative 1), (negative 2, 0), (negative 1, 1), (0, 2), (1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8), (7, 9), and (8, 10).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_205_img_new.jpg\" alt=\"Graph of the equation y = x + 2.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"height: 336px; width: 49.7484%;\">6.\n\n<span id=\"fs-id1169594206333\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 10, 7), (negative 9, 6), (negative 8, 5), (negative 7, 4), (negative 6, 3), (negative 5, 2), (negative 4, 1), (negative 3, 0), (negative 2, negative 1), (negative 1, negative 2), (0, negative 3), (1, negative 4), (2, negative 5), (3, negative 6), (4, negative 7), (5, negative 8), (6, negative 9), and (7, negative 10).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_207_img_new.jpg\" alt=\"Graph of the equation y = \u2212x \u2212 3.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span>\n\n&nbsp;<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50.2516%; height: 16px;\">7.\n\n<span id=\"fs-id1169594206416\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 5, negative 10), (negative 4, negative 8), (negative 3, negative 6), (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4), (3, 6), (4, 8), and (5, 10).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_209_img_new.jpg\" alt=\"Graph of the equation y = 2x.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.7484%; height: 16px;\">8.\n\n<span id=\"fs-id1169596636216\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, 12), (negative 2, 8), (negative 1, 4), (0, 0), (1, negative 4), (2, negative 8), and (3, negative 12).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_211_img_new.jpg\" alt=\"Graph of the equation y = 3x.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50.2516%; height: 16px;\">9.\n\n<span id=\"fs-id1169594077765\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 12, negative 4), (negative 10, negative 3), (negative 8, negative 2), (negative 6, negative 1), (negative 4, 0), (negative 2, 1), (0, 2), (2, 3), (4, 4), (6, 5), (8, 6), and (10, 7).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_213_img_new.jpg\" alt=\"Graph of the equation y = 1 half x + 2.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.7484%; height: 16px;\">10.\n\n<span id=\"fs-id1169596662210\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, negative 9), (0, negative 5), (3, negative 1), (6, 3), and (9, 7).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_215_img_new.jpg\" alt=\"Graph of the equation y = 4 thirds x \u2212 5.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50.2516%; height: 16px;\">11.\n\n<span id=\"fs-id1169596662303\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 10, 5), (negative 5, 3), (0, 1), (5, negative 1), and (10, negative 3).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_217_img_new.jpg\" alt=\"Graph of the equation y = \u2212 2 fifths x + 1.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.7484%; height: 16px;\">12.\n\n<span id=\"fs-id1169596754110\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 6, 11), (negative 4, 8), (negative 2, 5), (0, 2), (2, negative 1), (4, negative 4), (6, negative 7), and (8, negative 10).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_219_img_new.jpg\" alt=\"Graph of the equation y = \u2212 3 halves x + 2.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50.2516%; height: 16px;\">13.\n\n<span id=\"fs-id1169594073660\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, 10), (negative 3, 9), (negative 2, 8), (negative 1, 7), (0, 6), (1, 5), (2, 4), (3, 3), (4, 2), (5, 1), (6, 0), (7, negative 1), (8, negative 2), (9, negative 3), and (10, negative 4).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_221_img_new.jpg\" alt=\"Graph of the equation x + y = 6.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.7484%; height: 16px;\">14.\n\n<span id=\"fs-id1169594150705\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 10, 7), (negative 9, 6), (negative 8, 5), (negative 7, 4), (negative 6, 3), (negative 5, 2), (negative 4, 1), (negative 3, 0), (negative 2, negative 1), (negative 1, negative 2), (0, negative 3), (1, negative 4), (2, negative 5), (3, negative 6), (4, negative 7), (5, negative 8), (6, negative 9), and (7, negative 10).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_223_img_new.jpg\" alt=\"Graph of the equation x + y = \u22123.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50.2516%; height: 16px;\">15.\n\n<span id=\"fs-id1169594150788\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 8, negative 10), (negative 7, negative 9), (negative 6, negative 8), (negative 5, negative 7), (negative 4, negative 6), (negative 3, negative 5), (negative 2, negative 4), (negative 1, negative 3), (0, negative 2), (1, negative 1), (2, 0), (3, 1), (4, 2), (5, 3), (6, 4), (7, 5), (8, 6), (9, 7), and (10, 8).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_225_img_new.jpg\" alt=\"Graph of the equation x \u2212 y = 2.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.7484%; height: 16px;\">16.\n\n<span id=\"fs-id1169594045893\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 9, negative 8), (negative 8, negative 7), (negative 7, negative 6), (negative 6, negative 5), (negative 5, negative 4), (negative 4, negative 3), (negative 3, negative 2), (negative 2, negative 1), (negative 1, 0), (0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9), and (9, 10).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_227_img_new.jpg\" alt=\"Graph of the equation x \u2212 y = \u22121.\" width=\"243\" height=\"249\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50.2516%; height: 16px;\">17.\n\n<span id=\"fs-id1169596441600\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to -7. The equation 3 x plus y equals 7 is graphed.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_229_img_new.jpg\" alt=\"Graph of the equation 3x + y = 7.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.7484%; height: 16px;\">18.\n\n<span id=\"fs-id1169596441683\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 5, 7), (negative 4, 5), (negative 3, 3), (negative 2, 1), (negative 1, negative 1), (0, negative 3), (1, negative 5), and (2, negative 7).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_231_img_new.jpg\" alt=\"Graph of the equation 2x + y = \u22123.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50.2516%; height: 16px;\">&nbsp;\n\n19.\n\n<img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_233_img_new.jpg\" alt=\"Graph of the equation 1 third x + y = 2.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\">\n\n&nbsp;<\/td>\n<td style=\"width: 49.7484%; height: 16px;\"><span id=\"fs-id1169596642392\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, 6), (negative 4, 5), (negative 2, 4), (0, 3), (2, 2), (4, 1), and (6, 0).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_268_img_new.jpg\" alt=\"Graph of the equation y = \u2212 1 half x + 3.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.2516%;\">21\n\n<span id=\"fs-id1169594031029\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 3, 6), (0, 4), (3, 2), and (6, 0).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_237_img_new.jpg\" alt=\"Graph of the equation 2x + 3y = 12.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.7484%;\">22.\n\n<span id=\"fs-id1169596766742\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 4, negative 6), (0, negative 3), (4, 0), and (8, 3).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_239_img_new.jpg\" alt=\"Graph of the equation 3x \u2212 4y = 12.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.2516%;\">23.\n\n<span id=\"fs-id1169594056421\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, negative three halves), (negative 3, negative 1), (0, negative one half), (3, 0), and (6, one half).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_262_img_new.jpg\" alt=\"Graph of the equation x \u2212 6y = 3.\" width=\"229\" height=\"235\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.7484%;\">24.\n\n<span id=\"fs-id1169594056507\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 2, 7), (0, 2), (2, negative 3), and (4, negative 8).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_264_img_new.jpg\" alt=\"Graph of the equation 3x + y = 2.\" width=\"229\" height=\"235\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.2516%;\">25.\n\n<span id=\"fs-id1169594193072\" data-type=\"media\" data-alt=\"The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (4, 0), (4, 1), (4, 2) and all points with first coordinate 4.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_241_img_new.jpg\" alt=\"Graph of the equation x = 4. The resulting line is vertical.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.7484%;\">26.\n\n<span id=\"fs-id1169596438663\" data-type=\"media\" data-alt=\"The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (negative 2, 0), (negative 2, 1), (negative 2, 2) and all points with first coordinate negative 2.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_243_img_new.jpg\" alt=\"Graph of the equation x = \u22122. The resulting line is vertical.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.2516%;\">27.\n\n<span id=\"fs-id1169596438733\" data-type=\"media\" data-alt=\"The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The horizontal line goes through the points (0, 3), (1, 3), (2, 3) and all points with second coordinate 3.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_245_img_new.jpg\" alt=\"Graph of the line y = 3. The resulting line is horizontal.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.7484%;\">28.\n\n<span id=\"fs-id1169594129360\" data-type=\"media\" data-alt=\"The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The horizontal line goes through the points (0, negative 5), (1, negative 5), (2, negative 5) and all points with second coordinate negative 5.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_247_img_new.jpg\" alt=\"Graph of the line y = \u22125. The resulting line is horizontal.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.2516%;\">29.\n\n<span id=\"fs-id1169594129434\" data-type=\"media\" data-alt=\"The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (7\/3, 0), (7\/3, 1), (7\/3, 2) and all points with first coordinate 7\/3.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_249_img_new.jpg\" alt=\"Graph of the equation x = 7 thirds. The resulting line is vertical.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.7484%;\">30.\n\n<span id=\"fs-id1169596635780\" data-type=\"media\" data-alt=\"The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The horizontal line goes through the points (0, negative 15\/4), (1, negative 15\/4), (2, negative 15\/4) and all points with second coordinate negative 15\/4.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_251_img_new.jpg\" alt=\"Graph of the equation y = \u2212 15 fourths. The resulting line is horizontal.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.2516%;\">31.\n\n<span id=\"fs-id1169594150826\" data-type=\"media\" data-alt=\"The figure shows a two straight lines drawn on the same x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. One line is a straight horizontal line going through the points (negative 4, 2) (0, 2), (4, 2), and all other points with second coordinate 2. The other line is a slanted line going through the points (negative 5, negative 10), (negative 4, negative 8), (negative 3, negative 6), (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4), (3, 6), (4, 8), and (5, 10).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_253_img_new.jpg\" alt=\"The equations y= 2x and y = 2 are graphed. The equation y = 2x is a slanted line while y = 2 is horizontal.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.7484%;\">32.\n\n<span id=\"fs-id1169594150935\" data-type=\"media\" data-alt=\"The figure shows a two straight lines drawn on the same x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. One line is a straight horizontal line going through the points (negative 4, negative one half) (0, negative one half), (4, negative one half), and all other points with second coordinate negative one half. The other line is a slanted line going through the points (negative 10, 5), (negative 8, 4), (negative 6, 3), (negative 4, 2), (negative 2, 1), (0, 0), (1, negative 2), (2, negative 4), (3, negative 6), (4, negative 8), and (5, negative 10).\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_255_img_new.jpg\" alt=\"The equations y = \u2212 1 half x and y = \u2212 1 half are graphed. The equation y = \u2212 1 half x is a slanted line while y = \u2212 1 half is horizontal.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.2516%;\">33. \\$722, \\$850, \\$978<span data-type=\"newline\">\n<\/span><span id=\"fs-id1169594149740\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from 0 to 1200 in increments of 100. The y-axis of the plane runs from 0 to 1000 in increments of 100. The straight line starts at the point (0, 594) and goes through the points (400, 722), (800, 850), and (1200, 978). The right end of the line has an arrow pointing up and to the right.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_257_img_new.jpg\" alt=\"Graph of the equation y = 594 + 0.32x.\" width=\"243\" height=\"205\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 49.7484%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>","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 it is expected that you will be able to:<\/p>\n<ul>\n<li>Recognize the relationship between the solutions of an equation and its graph.<\/li>\n<li>Graph a linear equation by plotting points.<\/li>\n<li>Graph vertical and horizontal lines.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Recognize the Relationship Between the Solutions of an Equation and its Graph<\/h1>\n<p id=\"fs-id1169596288680\">In the previous section, we found several solutions to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11dc2d3604131c2e789dafb672c0914b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>. They are listed in the table below. So, the ordered pairs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-559928bd7c8949c8342dd73437aef05a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#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\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bcfb46537bc87e905a152e0aeb5f6d71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"50\" style=\"vertical-align: -17px;\" \/> are some solutions to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11dc2d3604131c2e789dafb672c0914b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>. We can plot these solutions in the rectangular coordinate system as shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_001\">(Figure 1)<\/a>.<\/p>\n<table class=\"aligncenter\" style=\"height: 80px;\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation 3x plus 2y equals 6. The second row is a header row and it labels each column. The first column header is \u201cx\u201d, the second is \u201cy\u201d and the third is \u201c(x, y)\u201d. Under the first column are the numbers 0, 2, and 1. Under the second column are the numbers 3, 0, and three halves. Under the third column are the ordered pairs (0, 3), (2, 0), and (1, three halves).\">\n<caption><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11dc2d3604131c2e789dafb672c0914b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"height: 16px; width: 38.9062px;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td style=\"height: 16px; width: 132.906px;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td style=\"height: 16px; width: 238.906px;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"height: 16px; width: 38.9062px;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"height: 16px; width: 132.906px;\" data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td style=\"height: 16px; width: 238.906px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 style=\"height: 16px;\" valign=\"top\">\n<td style=\"height: 16px; width: 38.9062px;\" data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td style=\"height: 16px; width: 132.906px;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"height: 16px; width: 238.906px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-559928bd7c8949c8342dd73437aef05a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#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 style=\"height: 16px;\" valign=\"top\">\n<td style=\"height: 16px; width: 38.9062px;\" data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td style=\"height: 16px; width: 132.906px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6d841d87b9a5793727b0590b3272eb6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"height: 16px; width: 238.906px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bcfb46537bc87e905a152e0aeb5f6d71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"50\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div><\/div>\n<div id=\"CNX_ElemAlg_Figure_04_02_001\" class=\"bc-figure figure\">\n<figure style=\"width: 301px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2020\/08\/CNX_ElemAlg_Figure_04_02_001_img_new.jpg\" alt=\"A graph that plots the points (0, 3), (1, three halves), and (2, 0).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .1<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1169596395639\">Notice how the points line up perfectly? We connect the points with a line to get the graph of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11dc2d3604131c2e789dafb672c0914b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_002\">(Figure 2)<\/a>. Notice the arrows on the ends of each side of the line. These arrows indicate the line continues.<\/p>\n<div id=\"CNX_ElemAlg_Figure_04_02_002\" class=\"bc-figure figure\">\n<figure style=\"width: 301px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_002_img_new.jpg\" alt=\"Described in previous paragraph.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .2<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1169596498779\">Every point on the line is a solution of the equation. Also, every solution of this equation is a point on this line. Points <em data-effect=\"italics\">not<\/em> on the line are not solutions.<\/p>\n<p id=\"fs-id1169596621603\">Notice that the point whose coordinates are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> is on the line shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_003\">(Figure 3)<\/a>. If you substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> into the equation, you find that it is a solution to the equation.<\/p>\n<div id=\"CNX_ElemAlg_Figure_04_02_003\" class=\"bc-figure figure\">\n<figure style=\"width: 301px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_003_img_new.jpg\" alt=\"Graphs the equation 3x plus 2y equals 6. The points (negative 2, 6) and (4, 1) are plotted. The line goes through (\u22122, 6) but not (4, 1).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .3<\/figcaption><\/figure>\n<\/div>\n<p><span id=\"fs-id1169596295719\" data-type=\"media\" data-alt=\"The figure shows a series of equations to check if the ordered pair (negative 2, 6) is a solution to the equation 3x plus 2y equals 6. The first line states \u201cTest (negative 2, 6)\u201d. The negative 2 is colored blue and the 6 is colored red. The second line states the two- variable equation 3x plus 2y equals 6. The third line shows the ordered pair substituted into the two- variable equation resulting in 3(negative 2) plus 2(6) equals 6 where the negative 2 is colored blue to show it is the first component in the ordered pair and the 6 is red to show it is the second component in the ordered pair. The fourth line is the simplified equation negative 6 plus 12 equals 6. The fifth line is the further simplified equation 6equals6. A check mark is written next to the last equation to indicate it is a true statement and show that (negative 2, 6) is a solution to the equation 3x plus 2y equals 6.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_020_img_new.jpg\" alt=\"The figure shows a series of equations to check if the ordered pair (negative 2, 6) is a solution to the equation 3x plus 2y equals 6. The first line states \u201cTest (negative 2, 6)\u201d. The negative 2 is colored blue and the 6 is colored red. The second line states the two- variable equation 3x plus 2y equals 6. The third line shows the ordered pair substituted into the two- variable equation resulting in 3(negative 2) plus 2(6) equals 6 where the negative 2 is colored blue to show it is the first component in the ordered pair and the 6 is red to show it is the second component in the ordered pair. The fourth line is the simplified equation negative 6 plus 12 equals 6. The fifth line is the further simplified equation 6equals6. A check mark is written next to the last equation to indicate it is a true statement and show that (negative 2, 6) is a solution to the equation 3x plus 2y equals 6.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596704533\">So the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> is a solution to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11dc2d3604131c2e789dafb672c0914b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>. (The phrase \u201cthe point whose coordinates are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>\u201d is often shortened to \u201cthe point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>.\u201d)<\/p>\n<p><span id=\"fs-id1169596233549\" data-type=\"media\" data-alt=\"The figure shows a series of equations to check if the ordered pair (4, 1) is a solution to the equation 3x plus 2y equals 6. The first line states \u201cWhat about (4, 1)?\u201d. The 4 is colored blue and the 1 is colored red. The second line states the two- variable equation 3x plus 2y equals 6. The third line shows the ordered pair substituted into the two- variable equation resulting in 3(4) plus 2(1) equals 6 where the 4 is colored blue to show it is the first component in the ordered pair and the 1 is red to show it is the second component in the ordered pair. The fourth line is the simplified equation 12 plus 2 equals 6. A question mark is placed above the equals sign to indicate that it is not known if the equation is true or false. The fifth line is the further simplified statement 14 not equal to 6. A \u201cnot equals\u201d sign is written between the two numbers and looks like an equals sign with a forward slash through it.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_021_img_new.jpg\" alt=\"The figure shows a series of equations to check if the ordered pair (4, 1) is a solution to the equation 3x plus 2y equals 6. The first line states \u201cWhat about (4, 1)?\u201d. The 4 is colored blue and the 1 is colored red. The second line states the two- variable equation 3x plus 2y equals 6. The third line shows the ordered pair substituted into the two- variable equation resulting in 3(4) plus 2(1) equals 6 where the 4 is colored blue to show it is the first component in the ordered pair and the 1 is red to show it is the second component in the ordered pair. The fourth line is the simplified equation 12 plus 2 equals 6. A question mark is placed above the equals sign to indicate that it is not known if the equation is true or false. The fifth line is the further simplified statement 14 not equal to 6. A \u201cnot equals\u201d sign is written between the two numbers and looks like an equals sign with a forward slash through it.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596211761\">So <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-da4dc2348b880aa050a82db91856c8b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> is not a solution to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11dc2d3604131c2e789dafb672c0914b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>. Therefore, the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-da4dc2348b880aa050a82db91856c8b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> is not on the line. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_002\">(Figure 2)<\/a>. This is an example of the saying, \u201cA picture is worth a thousand words.\u201d The line shows you <em data-effect=\"italics\">all<\/em> the solutions to the equation. Every point on the line is a solution of the equation. And, every solution of this equation is on this line. This line is called the <em data-effect=\"italics\">graph<\/em> of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11dc2d3604131c2e789dafb672c0914b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Graph of a linear equation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169594086156\">The <span data-type=\"term\">graph of a linear equation<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/> is a line.<\/p>\n<ul id=\"fs-id1169596469070\" data-bullet-style=\"bullet\">\n<li>Every point on the line is a solution of the equation.<\/li>\n<li>Every solution of this equation is a point on this line.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596301929\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596364071\" data-type=\"exercise\">\n<div id=\"fs-id1169596232522\" data-type=\"problem\">\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-id1169596446085\" data-type=\"problem\">\n<p id=\"fs-id1169596590486\">The graph of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> is shown.<\/p>\n<p><span data-type=\"media\" data-alt=\"The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line has a positive slope and goes through the y-axis at the (0, negative 3). The line is labeled with the equation y equals 2x negative 3.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_004_img_new.jpg\" alt=\"Graphs the line 2x\u22123.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169594147325\">For each ordered pair, decide:<\/p>\n<p id=\"fs-id1168464057467\"><span class=\"token\">a)<\/span>\u00a0Is the ordered pair a solution to the equation?<span data-type=\"newline\"><br \/>\n<\/span>b) Is the point on the line?<\/p>\n<p id=\"fs-id1169594053219\">A <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>\u2003B <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>\u2003C <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>\u2003D <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d66960a9b4adfa7702388a061d743cbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#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-id1169596584660\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\">\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<p id=\"fs-id1169594031478\">Substitute the <em data-effect=\"italics\">x<\/em>&#8211; and <em data-effect=\"italics\">y<\/em>&#8211; values into the equation to check if the ordered pair is a solution to the equation.<\/p>\n<p><span class=\"token\">a)<\/span><span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1169594053171\" data-type=\"media\" data-alt=\"The figure shows a series of equations to check if the ordered pairs (0, negative 3), (3, 3), (2, negative 3), and (negative 1, negative 5) are a solutions to the equation y equals 2x negative 3. The first line states the ordered pairs with the labels A: (0, negative 3), B: (3, 3), C: (2, negative 3), and D: (negative 1, negative 5). The first components are colored blue and the second components are colored red. The second line states the two- variable equation y equals 2x minus 3. The third line shows the four ordered pairs substituted into the two- variable equation resulting in four equations. The first equation is negative 3 equals 2(0) minus 3 where the 0 is colored clue and the negative 3 on the left side of the equation is colored red. The second equation is 3 equals 2(3) minus 3 where the 3 in parentheses is colored clue and the 3 on the left side of the equation is colored red. The third equation is negative 3 equals 2(2) minus 3 where the 2 in parentheses is colored clue and the negative 3 on the left side of the equation is colored red. The fourth equation is negative 5 equals 2(negative 1) minus 3 where the negative 1 is colored clue and the negative 5 is colored red. Question marks are placed above all the equal signs to indicate that it is not known if the equations are true or false. The fourth line shows the simplified versions of the four equations. The first is negative 3 equals negative 3 with a check mark indicating (0, negative 3) is a solution. The second is 3 equals 3 with a check mark indicating (3, 3) is a solution. The third is negative 3 not equals 1 indicating (2, negative 3) is not a solution. The fourth is negative 5 equals negative 5 with a check mark indicating (negative 1, negative 5) is a solution.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_022_img_new.jpg\" alt=\"The figure shows a series of equations to check if the ordered pairs (0, negative 3), (3, 3), (2, negative 3), and (negative 1, negative 5) are a solutions to the equation y equals 2x negative 3. The first line states the ordered pairs with the labels A: (0, negative 3), B: (3, 3), C: (2, negative 3), and D: (negative 1, negative 5). The first components are colored blue and the second components are colored red. The second line states the two- variable equation y equals 2x minus 3. The third line shows the four ordered pairs substituted into the two- variable equation resulting in four equations. The first equation is negative 3 equals 2(0) minus 3 where the 0 is colored clue and the negative 3 on the left side of the equation is colored red. The second equation is 3 equals 2(3) minus 3 where the 3 in parentheses is colored clue and the 3 on the left side of the equation is colored red. The third equation is negative 3 equals 2(2) minus 3 where the 2 in parentheses is colored clue and the negative 3 on the left side of the equation is colored red. The fourth equation is negative 5 equals 2(negative 1) minus 3 where the negative 1 is colored clue and the negative 5 is colored red. Question marks are placed above all the equal signs to indicate that it is not known if the equations are true or false. The fourth line shows the simplified versions of the four equations. The first is negative 3 equals negative 3 with a check mark indicating (0, negative 3) is a solution. The second is 3 equals 3 with a check mark indicating (3, 3) is a solution. The third is negative 3 not equals 1 indicating (2, negative 3) is not a solution. The fourth is negative 5 equals negative 5 with a check mark indicating (negative 1, negative 5) is a solution.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p>b) Plot the points A <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, B <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, C <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, and D <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d66960a9b4adfa7702388a061d743cbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/>.<span data-type=\"newline\"><br \/>\n<\/span> <span id=\"fs-id1169594085144\" data-type=\"media\" data-alt=\"The figure shows a straight line and four points and on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the two points and are labeled by the coordinates (negative 1, negative 5), (0, negative 3), (2, negative 3), and (3, 3). The straight line, labeled with the equation y equals 2x negative 3 goes through the three points (negative 1, negative 5), (0, negative 3), and (3, 3) but does not go through the point (2, negative 3).\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_005_img_new.jpg\" alt=\"Graph of the equation 2x\u22123. The points described in the previous paragraph are plotted.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596380866\">The points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d66960a9b4adfa7702388a061d743cbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> are on the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e09b4ae6d312635fcb8ec259a322e66d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/>, and the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> is not on the line.<\/p>\n<p id=\"fs-id1169596307156\">The points that are solutions to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> are on the line, but the point that is not a solution is not on the 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 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596301929\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596364071\" data-type=\"exercise\">\n<div id=\"fs-id1169596232522\" data-type=\"problem\">\n<p id=\"fs-id1169596679540\">Use the graph of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> to decide whether each ordered pair is:<\/p>\n<ul id=\"fs-id1169596240370\" data-bullet-style=\"bullet\">\n<li>a solution to the equation.<\/li>\n<li>on the line.<\/li>\n<\/ul>\n<p id=\"fs-id1169596497114\"><span class=\"token\">a) <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>\u2003b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/p>\n<p><span id=\"fs-id1169596375599\" data-type=\"media\" data-alt=\"The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the point (negative 2, negative 7) and for every 3 units it goes up, it goes one unit to the right. The line is labeled with the equation y equals 3x minus 1.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_006_img_new.jpg\" alt=\"Graph of the equation y = 3x\u22121.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id1169596446214\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596497874\"><span class=\"token\">a)<\/span> yes, yes\u2003b) yes, yes<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596243367\" class=\"bc-section section\" data-depth=\"1\">\n<h1 data-type=\"title\">Graph a Linear Equation by Plotting Points<\/h1>\n<p id=\"fs-id1169596531943\">There are several methods that can be used to graph a linear equation. The method we used to graph <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11dc2d3604131c2e789dafb672c0914b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/> is called plotting points, or the Point\u2013Plotting Method.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How To Graph an Equation By Plotting Points<\/div>\n<div id=\"fs-id1169596519072\" data-type=\"exercise\">\n<div id=\"fs-id1169596373126\" data-type=\"problem\">\n<p id=\"fs-id1169594153320\">Graph the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8af503cd473a72e30e30c2d46c7575ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/> by plotting points.<\/p>\n<\/div>\n<div id=\"fs-id1169596222394\" 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-id1169596298191\" data-type=\"media\" data-alt=\"The figure shows the three step procedure for graphing a line from the equation using the example equation y equals 2x minus 1. The first step is to \u201cFind three points whose coordinates are solutions to the equation. Organize the solutions in a table\u201d. The remark is made that \u201cYou can choose any values for x or y. In this case, since y is isolated on the left side of the equation, it is easier to choose values for x\u201d. The work for the first step of the example is shown through a series of equations aligned vertically. From the top down, the equations are y equals 2x plus 1, x equals 0 (where the 0 is blue), y equals 2x plus 1, y equals 2(0) plus 1 (where the 0 is blue), y equals 0 plus 1, y equals 1, x equals 1 (where the 1 is blue), y equals 2x plus 1, y equals 2(1) plus 1 (where the 1 is blue), y equals 2 plus 1, y equals 3, x equals negative 2 (where the negative 2 is blue), y equals 2x plus 1, y equals 2(negative 2) plus 1 (where the negative 2 is blue), y equals negative 4 plus 1, y equals negative 3. The work is then organized in a table. The table has 5 rows and 3 columns. The first row is a title row with the equation y equals 2x plus 1. The second row is a header row and it labels each column. The first column header is \u201cx\u201d, the second is \u201cy\u201d and the third is \u201c(x, y)\u201d. Under the first column are the numbers 0, 1, and negative 2. Under the second column are the numbers 1, 3, and negative 3. Under the third column are the ordered pairs (0, 1), (1, 3), and (negative 2, negative 3).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_044a_img_new.jpg\" alt=\"The figure shows the three step procedure for graphing a line from the equation using the example equation y equals 2x minus 1. The first step is to \u201cFind three points whose coordinates are solutions to the equation. Organize the solutions in a table\u201d. The remark is made that \u201cYou can choose any values for x or y. In this case, since y is isolated on the left side of the equation, it is easier to choose values for x\u201d. The work for the first step of the example is shown through a series of equations aligned vertically. From the top down, the equations are y equals 2x plus 1, x equals 0 (where the 0 is blue), y equals 2x plus 1, y equals 2(0) plus 1 (where the 0 is blue), y equals 0 plus 1, y equals 1, x equals 1 (where the 1 is blue), y equals 2x plus 1, y equals 2(1) plus 1 (where the 1 is blue), y equals 2 plus 1, y equals 3, x equals negative 2 (where the negative 2 is blue), y equals 2x plus 1, y equals 2(negative 2) plus 1 (where the negative 2 is blue), y equals negative 4 plus 1, y equals negative 3. The work is then organized in a table. The table has 5 rows and 3 columns. The first row is a title row with the equation y equals 2x plus 1. The second row is a header row and it labels each column. The first column header is \u201cx\u201d, the second is \u201cy\u201d and the third is \u201c(x, y)\u201d. Under the first column are the numbers 0, 1, and negative 2. Under the second column are the numbers 1, 3, and negative 3. Under the third column are the ordered pairs (0, 1), (1, 3), and (negative 2, negative 3).\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596685141\" data-type=\"media\" data-alt=\"The second step is to \u201cPlot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work!\u201d For the example the points are (0, 1), (1, 3), and (negative 2, negative 3). A graph shows the three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points at (0, 1), (1, 3), and (negative 2, negative 3). The question \u201cDo the points line up?\u201d is stated and followed with the answer \u201cYes, the points line up.\u201d\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_044b_img_new.jpg\" alt=\"The second step is to \u201cPlot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work!\u201d For the example the points are (0, 1), (1, 3), and (negative 2, negative 3). A graph shows the three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points at (0, 1), (1, 3), and (negative 2, negative 3). The question \u201cDo the points line up?\u201d is stated and followed with the answer \u201cYes, the points line up.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596291701\" data-type=\"media\" data-alt=\"The third step of the procedure is \u201cDraw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.\u201d A graph shows a straight line drawn through three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points at (0, 1), (1, 3), and (negative 2, negative 3). A straight line goes through all three points. The line has arrows on both ends pointing to the edge of the figure. The line is labeled with the equation y equals 2x plus 1. The statement \u201cThis line is the graph of y equals 2x plus 1\u201d is included next to the graph.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_044c_img_new.jpg\" alt=\"The third step of the procedure is \u201cDraw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.\u201d A graph shows a straight line drawn through three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points at (0, 1), (1, 3), and (negative 2, negative 3). A straight line goes through all three points. The line has arrows on both ends pointing to the edge of the figure. The line is labeled with the equation y equals 2x plus 1. The statement \u201cThis line is the graph of y equals 2x plus 1\u201d is included next to the graph.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596443288\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596764471\" data-type=\"exercise\">\n<div id=\"fs-id1169594155415\" data-type=\"problem\">\n<p id=\"fs-id1169596531818\">Graph the equation by plotting points: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596232896\" data-type=\"solution\"><span id=\"fs-id1169596438179\" data-type=\"media\" data-alt=\"The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 2, negative 7), (negative 1, negative 5), (0, negative 3), (1, negative 1), (2, 1), (3, 3), (4, 5), and (5, 7). There are arrows at the ends of the line pointing to the outside of the figure.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_023_img_new.jpg\" alt=\"Graph of the equation y = 2x\u22123.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596316200\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594076642\" data-type=\"exercise\">\n<div id=\"fs-id1169596534537\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Graph a linear equation by plotting points.<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596453724\">The steps to take when graphing a linear equation by plotting points are summarized below.<\/p>\n<div id=\"fs-id1169596686979\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\"><\/div>\n<ol id=\"fs-id1169596686441\" class=\"stepwise\" type=\"1\">\n<li>Find three points whose coordinates are solutions to the equation. Organize them in a table.<\/li>\n<li>Plot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work.<\/li>\n<li>Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596338664\">It is true that it only takes two points to determine a line, but it is a good habit to use three points. If you only plot two points and one of them is incorrect, you can still draw a line but it will not represent the solutions to the equation. It will be the wrong line.<\/p>\n<p id=\"fs-id1169594031834\">If you use three points, and one is incorrect, the points will not line up. This tells you something is wrong and you need to check your work. Look at the difference between part (a) and part (b) in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_010\">(Figure 4)<\/a>.<\/p>\n<div id=\"CNX_ElemAlg_Figure_04_02_010\" class=\"bc-figure figure\">\n<figure style=\"width: 403px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_010_img_new.jpg\" alt=\"Figure a shows three points with a straight line through them. Figure b shows three points that do not lie on the same line.\" width=\"403\" height=\"165\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .4<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1169596410945\">Let\u2019s do another example. This time, we\u2019ll show the last two steps all on one grid.<\/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<p>Graph the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ae17fd29062052621010e587cc571ee5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div id=\"fs-id1169596340938\" data-type=\"solution\">\n<div data-type=\"title\">Solution<\/div>\n<p id=\"fs-id1169596369626\">Find three points that are solutions to the equation. Here, again, it\u2019s easier to choose values for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>. Do you see why?<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<p><span id=\"fs-id1169594239630\" data-type=\"media\" data-alt=\"The figure shows three sets of equations used to determine ordered pairs from the equation y equals negative 3x. The first set has the equations: x equals 0 (where the 0 is blue), y equals negative 3x, y equals negative 3(0) (where the 0 is blue), y equals 0. The second set has the equations: x equals 1 (where the 1 is blue), y equals negative 3x, y equals negative 3(1) (where the 1 is blue), y equals negative 3. The third set has the equations: x equals negative 2 (where the negative 2 is blue), y equals negative 3x, y equals negative 3(negative 2) (where the negative 2 is blue), y equals 6.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_025_img_new.jpg\" alt=\"The figure shows three sets of equations used to determine ordered pairs from the equation y equals negative 3x. The first set has the equations: x equals 0 (where the 0 is blue), y equals negative 3x, y equals negative 3(0) (where the 0 is blue), y equals 0. The second set has the equations: x equals 1 (where the 1 is blue), y equals negative 3x, y equals negative 3(1) (where the 1 is blue), y equals negative 3. The third set has the equations: x equals negative 2 (where the negative 2 is blue), y equals negative 3x, y equals negative 3(negative 2) (where the negative 2 is blue), y equals 6.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596518462\">We list the points in the table below.<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<table id=\"fs-id1169596654135\" class=\"grid\" style=\"width: 100%;\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation y equals negative 3x. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 1, and negative 2. Under the second column are the numbers 0, negative 3, and 6. Under the third column are the ordered pairs (0, 0), (1, negative 3), and (negative 2, 6).\">\n<caption><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ae17fd29062052621010e587cc571ee5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\">6<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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<\/tbody>\n<\/table>\n<p id=\"fs-id1169596275520\">Plot the points, check that they line up, and draw the line.<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<p><span id=\"fs-id1169596310903\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn through three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points which are labeled by their ordered pairs (negative 2, 6), (0, 0), and (1, negative 3). A straight line goes through all three points. The line has arrows on both ends pointing to the outside of the figure. The line is labeled with the equation y equals negative 3x.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_011_img_new.jpg\" alt=\"Graph of the equation y = \u22123x. The points listed in the previous table are plotted.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\" \/><\/span><\/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 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596656657\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594157527\" data-type=\"exercise\">\n<div id=\"fs-id1169594159171\" data-type=\"problem\">\n<p id=\"fs-id1169594150201\">Graph the equation by plotting points: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169594085758\" data-type=\"solution\"><span id=\"fs-id1169596704588\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 2, 8), (0, 0), and (2, negative 8). The line has arrows on both ends pointing to the outside of the figure.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_012_img_new.jpg\" alt=\"A graph of the equation y = \u22124x.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\">\n<p>When an equation includes a fraction as the coefficient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, we can still substitute any numbers for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>. But the math is easier if we make \u2018good\u2019 choices for the values of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>. This way we will avoid fraction answers, which are hard to graph precisely.<\/p>\n<\/div>\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-id1169596362679\" data-type=\"problem\">\n<p id=\"fs-id1169596702145\">Graph the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fe4c81cc2a658e51ba14155245da8746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594002064\" 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-id1169596299233\">Find three points that are solutions to the equation. Since this equation has the fraction <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5aa3fe0ad89cf65f34b5c880c078356e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\" \/> as a coefficient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-038741496726a75b03e91a2e030b0287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\" \/> we will choose values of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> carefully. We will use zero as one choice and multiples of 2 for the other choices. Why are multiples of 2 a good choice for values of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>?<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<p><span id=\"fs-id1169596440466\" data-type=\"media\" data-alt=\"The figure shows three sets of equations used to determine ordered pairs from the equation y equals (one half)x plus 3. The first set has the equations: x equals 0 (where the 0 is blue), y equals (one half)x plus 3, y equals (one half)(0) plus 3 (where the 0 is blue), y equals 0 plus 3, y equals 3. The second set has the equations: x equals 2 (where the 2 is blue), y equals (one half)x plus 3, y equals (one half)(2) plus 3 (where the 2 is blue), y equals 1 plus 3, y equals 4. The third set has the equations: x equals 4 (where the 4 is blue), y equals (one half)x plus 3, y equals (one half)(4) plus 3 (where the 4 is blue), y equals 2 plus 3, y equals 5.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_026_img_new.jpg\" alt=\"The figure shows three sets of equations used to determine ordered pairs from the equation y equals (one half)x plus 3. The first set has the equations: x equals 0 (where the 0 is blue), y equals (one half)x plus 3, y equals (one half)(0) plus 3 (where the 0 is blue), y equals 0 plus 3, y equals 3. The second set has the equations: x equals 2 (where the 2 is blue), y equals (one half)x plus 3, y equals (one half)(2) plus 3 (where the 2 is blue), y equals 1 plus 3, y equals 4. The third set has the equations: x equals 4 (where the 4 is blue), y equals (one half)x plus 3, y equals (one half)(4) plus 3 (where the 4 is blue), y equals 2 plus 3, y equals 5.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169594086177\">The points are shown in the table below.<\/p>\n<table id=\"fs-id1169596641191\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation y equals (one half)x plus 3. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 2, and 4. Under the second column are the numbers 3, 4, and 5. Under the third column are the ordered pairs (0, 3), (2, 4), and (4, 5).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fe4c81cc2a658e51ba14155245da8746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\" \/><\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-65c84a7e1d884e51e9ff8e8338318a74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#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<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">5<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b385c1ebb27da6a9f60a8f21a49f0483_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#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<\/tbody>\n<\/table>\n<p id=\"fs-id1169594156783\">Plot the points, check that they line up, and draw the line.<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<p><span id=\"fs-id1169594189788\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn through three points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the three points which are labeled by their ordered pairs (0, 3), (2, 4), and (4, 5). A straight line goes through all three points. The line has arrows on both ends pointing to the outside of the figure. The line is labeled with the equation y equals (one half)x plus 3.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_014_img_new.jpg\" alt=\"The points listed in the previous table are plotted. The equation y = 1 half x + 3 is graphed.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\" \/><\/span><\/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 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596392359\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596392362\" data-type=\"exercise\">\n<div id=\"fs-id1169596392364\" data-type=\"problem\">\n<p id=\"fs-id1169594004706\">Graph the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a52fc6d8b40edcd095f7949c7a07b155_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;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596565866\" data-type=\"solution\"><span id=\"fs-id1169596439026\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 9, negative 4), (negative 6, negative 3), (negative 3, negative 2), (0, negative 1), (3, 0), (6, 1), and (9, 2). The line has arrows on both ends pointing to the outside of the figure.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_015_img_new.jpg\" alt=\"A graph of the equation y = 1 third x\u22121.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596686309\">So far, all the equations we graphed had <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> given in terms of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>. Now we\u2019ll graph an equation with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> on the same side. Let\u2019s see what happens in the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cd15f85ef01304a23f7bb2c1cbd81070_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/>. If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5e8ef70615fdaee8588017ac1fdd2da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/> what is the value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>?<\/p>\n<p><span id=\"fs-id1169596445877\" data-type=\"media\" data-alt=\"The figure shows a set of equations used to determine an ordered pair from the equation 2x plus y equals 3. The first equation is y equals 0 (where the 0 is red). The second equation is the two- variable equation 2x plus y equals 3. The third equation is the onenegative variable equation 2x plus 0 equals 3 (where the 0 is red). The fourth equation is 2x equals 3. The fifth equation is x equals three halves. The last line is the ordered pair (three halves, 0).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_027_img_new.jpg\" alt=\"The figure shows a set of equations used to determine an ordered pair from the equation 2x plus y equals 3. The first equation is y equals 0 (where the 0 is red). The second equation is the two- variable equation 2x plus y equals 3. The third equation is the onenegative variable equation 2x plus 0 equals 3 (where the 0 is red). The fourth equation is 2x equals 3. The fifth equation is x equals three halves. The last line is the ordered pair (three halves, 0).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596445921\">This point has a fraction for the <em data-effect=\"italics\">x<\/em>&#8211; coordinate and, while we could graph this point, it is hard to be precise graphing fractions. Remember in the example <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fe4c81cc2a658e51ba14155245da8746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"87\" style=\"vertical-align: -12px;\" \/>, we carefully chose values for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> so as not to graph fractions at all. If we solve the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cd15f85ef01304a23f7bb2c1cbd81070_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, it will be easier to find three solutions to the equation.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ad50e6aa617c0497b2a6abb8e4f21d4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#120;&#43;&#121;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#121;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#50;&#120;&#43;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"160\" style=\"vertical-align: -15px;\" \/><\/p>\n<p id=\"fs-id1169596382780\">The solutions for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3330a01aa4d7d81947b71297d8623d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: -1px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ad143a0d979362a51b48a48c9ca9f59e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: -1px;\" \/> are shown in the table below. The graph is shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_017\">(Figure 5)<\/a>.<\/p>\n<table id=\"fs-id1169596387360\" class=\"aligncenter\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation 2x plus y equals 3. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 1, and negative 1. Under the second column are the numbers 3, 1, and 5. Under the third column are the ordered pairs (0, 3), (1, 1), and (negative 1, 5).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cd15f85ef01304a23f7bb2c1cbd81070_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-745bd1150b5c3e65ae8bad5282a5b3b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#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 valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\">5<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1c6cf6f67551105173d9fb3cab5966cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#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<\/tbody>\n<\/table>\n<div id=\"CNX_ElemAlg_Figure_04_02_017\" class=\"bc-figure figure\">\n<p>&nbsp;<\/p>\n<figure style=\"width: 362px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_017_img_new.jpg\" alt=\"The points listed in the previous table are plotted. The equation 2x + y = 3 is graphed.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .5<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1169596376662\">Can you locate the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0360b436d45119746628cab02a18fc91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"50\" style=\"vertical-align: -17px;\" \/>, which we found by letting <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5e8ef70615fdaee8588017ac1fdd2da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/>, on the line?<\/p>\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-id1169594029163\" data-type=\"problem\">\n<p id=\"fs-id1169594029165\">Graph the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5046b27d47eb2797e1efc80e3a349108_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596754513\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-846\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td>Find three points that are solutions to the equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6d11398243e3d2d898ad9234715550a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#121;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#61;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>First, solve the equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ed2476afbe0bf8779509f544eb1741c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#61;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#51;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596364491\">We\u2019ll let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> be 0, 1, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> to find 3 points. The ordered pairs are shown in the table below. Plot the points, check that they line up, and draw the line. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_018\">(Figure 6)<\/a>.<\/p>\n<table id=\"fs-id1169596364512\" class=\"aligncenter\" style=\"height: 70px; width: 100%;\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation 3x plus y equals negative 1. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 1, and negative 1. Under the second column are the numbers negative 1, negative 4, and 2. Under the third column are the ordered pairs (0, negative 1), (1, negative 4), and (negative 1, 2).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5046b27d47eb2797e1efc80e3a349108_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/strong><\/caption>\n<tbody>\n<tr style=\"height: 14px;\" valign=\"top\">\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td style=\"height: 14px; width: 238.406px;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\" valign=\"top\">\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td style=\"height: 14px; width: 238.406px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 style=\"height: 14px;\" valign=\"top\">\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td style=\"height: 14px; width: 238.406px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-95e282826e52860edf4d8703db75fb7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#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 style=\"height: 14px;\" valign=\"top\">\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td style=\"height: 14px; width: 78.4062px;\" data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td style=\"height: 14px; width: 238.406px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"CNX_ElemAlg_Figure_04_02_018\" class=\"bc-figure figure\">\n<figure style=\"width: 360px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_018_img_new.jpg\" alt=\"The points listed in the previous table are plotted. The equation 3x+y = \u22121 is graphed.\" width=\"360\" height=\"367\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .6<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596314007\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596314011\" data-type=\"exercise\">\n<div id=\"fs-id1169596314014\" data-type=\"problem\">\n<p id=\"fs-id1169596314016\">Graph the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1ed5c27006ba061a17ef6a7ec7aca351_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596314036\" data-type=\"solution\"><span id=\"fs-id1169596314039\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, 10), (negative 2, 6), (0, 2), (2, negative 2), (4, negative 6), and (6, negative 10). The line has arrows on both ends pointing to the outside of the figure.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_019_img_new.jpg\" alt=\"Graph of the equation 2 x + y = 2.\" width=\"243\" height=\"249\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\"><\/div>\n<\/div>\n<p id=\"fs-id1169596446914\">If you can choose any three points to graph a line, how will you know if your graph matches the one shown in the answers in the book? If the points where the graphs cross the <em data-effect=\"italics\">x<\/em>&#8211; and <em data-effect=\"italics\">y<\/em>-axis are the same, the graphs match!<\/p>\n<p id=\"fs-id1169596446930\">The equation in <a class=\"autogenerated-content\" href=\"#fs-id1169596376662\">(Example 5)<\/a> was written in standard form, with both <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> on the same side. We solved that equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> in just one step. But for other equations in standard form it is not that easy to solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, so we will leave them in standard form. We can still find a first point to plot by letting <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> and solving for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 can plot a second point by letting <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5e8ef70615fdaee8588017ac1fdd2da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/> and then solving for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>. Then we will plot a third point by using some other value for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596438837\" data-type=\"problem\">\n<p id=\"fs-id1169594030848\">Graph the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9989fe75c24aab1a670faf84c52a2776_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594030870\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-511\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td>Find three points that are solutions to the equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-38dce1297fb2cdb7d1b1a32fe1b284e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#120;&#45;&#51;&#121;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"114\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>First, let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8978bb005f14a6cc379422dcf21856b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#51;&#121;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b17305225cee2ac454a3073735d40418_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;&#45;&#51;&#121;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#121;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"99\" style=\"vertical-align: -15px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Now let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5e8ef70615fdaee8588017ac1fdd2da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1dd25c8db90481e8a1ec65a9c6654fe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#120;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0862bb2fdc5ca85ce60b737eef626553_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#120;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#120;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"74\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>We need a third point. Remember, we can choose any value for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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&#8217;ll let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-116dfacb4c2a32bdfb5ab9e852f29986_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d39c75569c92161bfb6bcdfb2c252357_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#51;&#121;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7dd56488e275f3d34d81d00d719e7696_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;&#49;&#50;&#45;&#51;&#121;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#51;&#121;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#121;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"126\" style=\"vertical-align: -26px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596548028\">We list the ordered pairs in the table below. Plot the points, check that they line up, and draw the line. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_029\">(Figure 7)<\/a>.<\/p>\n<table id=\"fs-id1169596548039\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation 2x negative 3y equals 6. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 3, and 6. Under the second column are the numbers negative 2, 0, and 2. Under the third column are the ordered pairs (0, negative 2), (3, 0), and (6, 2).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9989fe75c24aab1a670faf84c52a2776_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">6<\/td>\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"CNX_ElemAlg_Figure_04_02_029\" class=\"bc-figure figure\">\n<figure style=\"width: 362px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_029_img_new.jpg\" alt=\"The points listed in previous table are plotted. The equation 2x \u2212 3y = 6 is plotted.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .7<\/figcaption><\/figure>\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<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596381106\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596381110\" data-type=\"exercise\">\n<div id=\"fs-id1169596381112\" data-type=\"problem\">\n<p id=\"fs-id1169596381114\">Graph the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5d2f160a838866df1ddfcb4c97649376_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#50;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596381137\" data-type=\"solution\"><span id=\"fs-id1169596381140\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 1, 6), (0, 4), (1, 2), (2, 0), (3, negative 2), and (4, negative 4). The line has arrows on both ends pointing to the outside of the figure.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_030_img_new.jpg\" alt=\"Graph of the equation 4x + 2y = 8.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596381158\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596381162\" data-type=\"exercise\">\n<div id=\"fs-id1169596387128\" data-type=\"solution\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Graph Vertical and Horizontal Lines<\/h1>\n<p id=\"fs-id1169596387156\">Can we graph an equation with only one variable? Just <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 no <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, or just <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> without an <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>? How will we make a table of values to get the points to plot?<\/p>\n<p id=\"fs-id1169594240483\">Let\u2019s consider the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>. This equation has only one variable, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>. The equation says that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> is <em data-effect=\"italics\">always<\/em> equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, so its value does not depend on <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>. No matter what <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> is, the value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> is always <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>.<\/p>\n<p id=\"fs-id1169596226049\">So to make a table of values, write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> in for all the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> values. Then choose any values for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>. Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> does not depend on <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, you can choose any numbers you like. But to fit the points on our coordinate graph, we\u2019ll use 1, 2, and 3 for the <em data-effect=\"italics\">y<\/em>-coordinates. See the table below.<\/p>\n<table id=\"fs-id1169596226086\" class=\"aligncenter\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation x equals negative 3. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers negative 3, negative 3, and negative 3. Under the second column are the numbers 1, 2, and 3. Under the third column are the ordered pairs (negative 3, 1), (negative 3, 2), and (negative 3, 3).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0e0819cfb987fa92d333add15bb2e864_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#49;&#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 valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-03125d47f1e456b2a5c3479daa28f59c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#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<\/tbody>\n<\/table>\n<p id=\"fs-id1169594079050\">Plot the points from the table and connect them with a straight line. Notice in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_032\">(Figure 8)<\/a> that we have graphed a <em data-effect=\"italics\">vertical line<\/em>.<\/p>\n<div id=\"CNX_ElemAlg_Figure_04_02_032\" class=\"bc-figure figure\">\n<figure style=\"width: 362px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_032_img_new.jpg\" alt=\"The points listed in the previous table are plotted. The equation x = \u22123 is graphed. The resulting line is vertical.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .8<\/figcaption><\/figure>\n<\/div>\n<div id=\"fs-id1169594079091\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Vertical line<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169594178158\">A <span data-type=\"term\">vertical line<\/span> is the graph of an equation of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>.<\/p>\n<p id=\"fs-id1169594178174\">The line passes through the <em data-effect=\"italics\">x<\/em>-axis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-53d4347201ab8f9c6f195eeec4b01f0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#44;&#48;&#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>\n<\/div>\n<div data-type=\"title\">\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-id1169594178204\" data-type=\"problem\">\n<p id=\"fs-id1169594178206\">Graph the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594150626\" 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-id1169594150632\">The equation has only one variable, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> is always equal to 2. We create the table below where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> is always 2 and then put in any values for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>. The graph is a vertical line passing through the <em data-effect=\"italics\">x<\/em>-axis at 2. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_033\">(Figure 9)<\/a>.<\/p>\n<table id=\"fs-id1169594150665\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation x equals 2. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 2, 2, and 2. Under the second column are the numbers 1, 2, and 3. Under the third column are the ordered pairs (2, 1), (2, 2), and (2, 3).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3fca1a384cf5042876a719066cbbb127_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#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<\/tbody>\n<\/table>\n<div id=\"CNX_ElemAlg_Figure_04_02_033\" class=\"bc-figure figure\" style=\"text-align: center;\">\n<figure style=\"width: 362px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_033_img_new.jpg\" alt=\"The points listed in the previous table are plotted. The equation x = 2 is graphed. The resulting line is vertical.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .9<\/figcaption><\/figure>\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<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594129269\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594129273\" data-type=\"exercise\">\n<div id=\"fs-id1169594129275\" data-type=\"problem\">\n<p id=\"fs-id1169594129277\">Graph the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169594129291\" data-type=\"solution\"><span id=\"fs-id1169594129294\" data-type=\"media\" data-alt=\"The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (5, 1), (5, 2), (5, 3), and all other points with first coordinate 5. The line has arrows on both ends pointing to the outside of the figure.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_034_img_new.jpg\" alt=\"Graph of the equation x = 5. The resulting line is vertical.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\">\n<p>What if the equation has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> but no <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>? Let\u2019s graph the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>. This time the <em>y<\/em>&#8211; value is a constant, so in this equation, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> does not depend on <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>. Fill in 4 for all the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>\u2019s in the table below and then choose any values for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>. We\u2019ll use 0, 2, and 4 for the <em>x<\/em>-coordinates.<\/p>\n<\/div>\n<\/div>\n<table id=\"fs-id1169594030456\" class=\"aligncenter\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation y equals 4. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 2, and 4. Under the second column are the numbers 4, 4, and 4. Under the third column are the ordered pairs (0, 4), (2, 4), and (4, 4).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-65c84a7e1d884e51e9ff8e8338318a74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#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<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9f071f7020da53c225631b96b8f9875e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#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<p id=\"fs-id1169596754204\">The graph is a horizontal line passing through the <em data-effect=\"italics\">y<\/em>-axis at 4. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_036\">(Figure 10)<\/a>.<\/p>\n<div id=\"CNX_ElemAlg_Figure_04_02_036\" class=\"bc-figure figure\">\n<figure style=\"width: 362px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_036_img_new.jpg\" alt=\"The points listed in the previous table are plotted. The equation y = 4 is graphed. The resulting line is horizontal.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .10<\/figcaption><\/figure>\n<\/div>\n<div id=\"fs-id1169596409604\" data-type=\"note\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Horizontal line<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596409609\">A <span data-type=\"term\">horizontal line<\/span> is the graph of an equation of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bfc522d71f8ae0353ab021fa2a90c360_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p id=\"fs-id1169596409625\">The line passes through the <em data-effect=\"italics\">y<\/em>-axis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-05dbabd42fe84ba97e673be0628c5974_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"37\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596409655\" data-type=\"problem\">\n<p id=\"fs-id1169596409657\">Graph the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1144e182f26c1fd5166b5411a3ed3cd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#49;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"60\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div 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-id1169596652714\">The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> has only one variable, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>. The value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> is constant. All the ordered pairs in the table below have the same <em data-effect=\"italics\">y<\/em>-coordinate. The graph is a horizontal line passing through the <em data-effect=\"italics\">y<\/em>-axis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, as shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_037\">(Figure 11)<\/a>.<\/p>\n<table style=\"width: 100%;\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation y equals negative 1. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 3, and negative 3. Under the second column are the numbers negative 1, negative 1, and negative 1. Under the third column are the ordered pairs (0, negative 1), (3, negative 1), and (negative 3, negative 1).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0d66a71b8940b998e4f29f8cccda06d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#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 valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"CNX_ElemAlg_Figure_04_02_037\" class=\"bc-figure figure\">\n<figure style=\"width: 362px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_037_img_new.jpg\" alt=\"The points listed in the previous table are plotted. The equation y = \u22121 is graphed. The resulting line is horizontal.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .11<\/figcaption><\/figure>\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<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594008580\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594008584\" data-type=\"exercise\">\n<div id=\"fs-id1169594008586\" data-type=\"problem\">\n<p id=\"fs-id1169594008588\">Graph the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169594008602\" data-type=\"solution\"><span id=\"fs-id1169594008605\" data-type=\"media\" data-alt=\"The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, negative 4), (0, negative 4), (4, negative 4), and all other points with second coordinate negative 4. The line has arrows on both ends pointing to the outside of the figure.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_038_img_new.jpg\" alt=\"Graph of the equation y = \u22124. The resulting line is horizontal.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\">\n<p>The equations for vertical and horizontal lines look very similar to equations like <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-daf4fb55b4aeed3a4aa1689f9aa29cf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/> What is the difference between the equations <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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<\/div>\n<\/div>\n<p id=\"fs-id1169594123637\">The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> has both <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>. The value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> depends on the value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>. The <em data-effect=\"italics\">y<\/em>-coordinate changes according to the value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> has only one variable. The value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> is constant. The <em data-effect=\"italics\">y<\/em>-coordinate is always 4. It does not depend on the value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>. See the tables below.<\/p>\n<table id=\"fs-id1169594030456\" class=\"aligncenter\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation y equals 4. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 2, and 4. Under the second column are the numbers 4, 4, and 4. Under the third column are the ordered pairs (0, 4), (2, 4), and (4, 4).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-65c84a7e1d884e51e9ff8e8338318a74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#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<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9f071f7020da53c225631b96b8f9875e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#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<div>\n<table id=\"fs-id1169594030456\" class=\"aligncenter\" summary=\"This table has 5 rows and 3 columns. The first row is a title row with the equation y equals 4. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 2, and 4. Under the second column are the numbers 4, 4, and 4. Under the third column are the ordered pairs (0, 4), (2, 4), and (4, 4).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/caption>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">8<\/td>\n<td data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-73e99ec02208b21faacd2a1bb57fbe83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#56;&#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<\/div>\n<div id=\"CNX_ElemAlg_Figure_04_02_040\" class=\"bc-figure figure\">\n<figure style=\"width: 362px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_040_img_new.jpg\" alt=\"The equations y = 4 and y = 4x are graphed and labelled.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .12<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1169594034174\">Notice, in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_040\">(Figure 12)<\/a>, the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> gives a slanted line, while <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> gives a horizontal line.<\/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 id=\"fs-id1169596446108\" data-type=\"problem\">\n<p id=\"fs-id1169596446110\">Graph <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ae17fd29062052621010e587cc571ee5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> in the same rectangular coordinate system.<\/p>\n<\/div>\n<div id=\"fs-id1169596446136\" 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-id1169596446141\">Notice that the first equation has the variable <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, while the second does not. See the tables below. The two graphs are shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_02_041\">(Figure 13)<\/a>.<\/p>\n<div>\n<table id=\"fs-id1169596446157\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"There are two tables, each with 5 rows and 3 columns. For the table on the left: The first row is a title row with the equation y equals negative 3x. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 1, and 2. Under the second column are the numbers 0, negative 3, and negative 6. Under the third column are the ordered pairs (0, 0), (1, negative 3), and (2, negative 6). For the table on the right: The first row is a title row with the equation y equals negative 3. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 1, and 2. Under the second column are the numbers negative 3, negative 3, and negative 3. Under the third column are the ordered pairs (0, negative 3), (1, negative 3), and (2, negative 3).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ae17fd29062052621010e587cc571ee5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 40px; height: 16px;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td style=\"width: 47px; height: 16px;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td style=\"width: 125px; height: 16px;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 40px; height: 16px;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 47px; height: 16px;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 125px; height: 16px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 40px; height: 16px;\" data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td style=\"width: 47px; height: 16px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td style=\"width: 125px; height: 16px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 40px; height: 16px;\" data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td style=\"width: 47px; height: 16px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 125px; height: 16px;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bc5a1a3641d8f02029c43e39946295c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#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<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"fs-id1169596446157\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"There are two tables, each with 5 rows and 3 columns. For the table on the left: The first row is a title row with the equation y equals negative 3x. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 1, and 2. Under the second column are the numbers 0, negative 3, and negative 6. Under the third column are the ordered pairs (0, 0), (1, negative 3), and (2, negative 6). For the table on the right: The first row is a title row with the equation y equals negative 3. The second row is a header row and it labels each column. The first column header is x, the second is y and the third is (x, y). Under the first column are the numbers 0, 1, and 2. Under the second column are the numbers negative 3, negative 3, and negative 3. Under the third column are the ordered pairs (0, negative 3), (1, negative 3), and (2, negative 3).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 41px; height: 16px;\" data-align=\"center\" data-valign=\"top\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td style=\"width: 46px; height: 16px;\" data-align=\"center\" data-valign=\"top\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<td style=\"width: 126px; height: 16px;\" data-align=\"center\" data-valign=\"top\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 41px; height: 16px;\" data-align=\"center\" data-valign=\"top\">0<\/td>\n<td style=\"width: 46px; height: 16px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td style=\"width: 126px; height: 16px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 41px; height: 16px;\" data-align=\"center\" data-valign=\"top\">1<\/td>\n<td style=\"width: 46px; height: 16px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td style=\"width: 126px; height: 16px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 41px; height: 16px;\" data-align=\"center\" data-valign=\"top\">2<\/td>\n<td style=\"width: 46px; height: 16px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/td>\n<td style=\"width: 126px; height: 16px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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<\/div>\n<div id=\"CNX_ElemAlg_Figure_04_02_041\" class=\"bc-figure figure\">\n<figure style=\"width: 362px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_041_img_new.jpg\" alt=\"The equations y = \u22123 and y = \u22123x are graphed and labelled. The equation y = \u22123x is a slanted line while y = \u22123 is horizontal.\" width=\"362\" height=\"369\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .13<\/figcaption><\/figure>\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<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596446275\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596446279\" data-type=\"exercise\">\n<div id=\"fs-id1169596446281\" data-type=\"problem\">\n<p id=\"fs-id1169596446283\">Graph <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> in the same rectangular coordinate system.<\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1169596446309\" data-type=\"solution\"><span id=\"fs-id1169596446312\" data-type=\"media\" data-alt=\"The figure shows a two straight lines drawn on the same x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. One line is a straight horizontal line going through the points (negative 4, negative 4), (0, negative 4), (4, negative 4), and all other points with second coordinate negative 4. The other line is a slanted line going through the points (negative 2, 8), (negative 1, 4), (0, 0), (1, negative 4), and (2, negative 8).\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_042_img_new.jpg\" alt=\"The equations y = \u22124 and y = \u22124x are graphed and labelled. The equation y = \u22124x is a slanted line while y = \u22124 is horizontal.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"fs-id1169594154430\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Graph a Linear Equation by Plotting Points<\/strong>\n<ol id=\"fs-id1169594079036\" class=\"stepwise\" type=\"1\">\n<li>Find three points whose coordinates are solutions to the equation. Organize them in a table.<\/li>\n<li>Plot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work!<\/li>\n<li>Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1 data-type=\"title\">Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1169594176658\">\n<dt>graph of a linear equation<\/dt>\n<dd id=\"fs-id1169594176664\">The graph of a linear equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/> is a straight line. Every point on the line is a solution of the equation. Every solution of this equation is a point on this line.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594176687\">\n<dt>horizontal line<\/dt>\n<dd id=\"fs-id1169594176692\">A horizontal line is the graph of an equation of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bfc522d71f8ae0353ab021fa2a90c360_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/>. The line passes through the <em data-effect=\"italics\">y<\/em>-axis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-05dbabd42fe84ba97e673be0628c5974_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"37\" style=\"vertical-align: -4px;\" \/>.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169596554286\">\n<dt>vertical line<\/dt>\n<dd id=\"fs-id1169596554292\">A vertical line is the graph of an equation of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>. The line passes through the <em data-effect=\"italics\">x<\/em>-axis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-53d4347201ab8f9c6f195eeec4b01f0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>.<\/dd>\n<\/dl>\n<\/div>\n<h1 data-type=\"title\">3.2 Exercise Set<\/h1>\n<p id=\"fs-id1169594212944\">In the following exercises, for each ordered pair, decide:<\/p>\n<p><span class=\"token\">a)<\/span> Is the ordered pair a solution to the equation?\u2003b) Is the point on the line?<\/p>\n<ol>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>\n<ol type=\"A\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c1d1c22dc2eabfdd66670fe21fd738b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<table class=\"aligncenter\" style=\"border-collapse: collapse; width: 45.0873%; height: 278px;\">\n<tbody>\n<tr>\n<td style=\"width: 100%;\"><span id=\"fs-id1169594008347\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, negative 4), (negative 5, negative 3), (negative 4, negative 2), (negative 3, negative 1), (negative 2, 0), (negative 1, 1), (0, 2), (1, 3), (2, 4), (3, 5), (4, 6), and (5, 7).\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_259_img_new.jpg\" alt=\"Graph of the equation y = x + 2.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol start=\"2\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>\n<ol type=\"A\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-da4dc2348b880aa050a82db91856c8b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<table class=\"aligncenter\" style=\"border-collapse: collapse; width: 28.3843%; height: 30px;\">\n<tbody>\n<tr>\n<td style=\"width: 100%;\"><span data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, negative 6), (negative 4, negative 5), (negative 2, negative 4), (0, negative 3), (2, negative 2), (4, negative 1), and (6, 0).\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_261_img_new.jpg\" alt=\"Graph of the equation y = 1 half x \u2212 3.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596319037\">In the following exercises, graph by plotting points.<\/p>\n<ol class=\"twocolumn\" start=\"3\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4ecf689c13800069b252cefb0f1d5b07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-90a3bd9d443d8f417af939f7c60966d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-46e2c585eded74b8bff6aa4416e3bf45_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;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"86\" style=\"vertical-align: -12px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9d76d654ea20e2e13278d2483a7b9ac9_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;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"99\" style=\"vertical-align: -12px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5663c8903e107d727050274d527d970d_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;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"99\" style=\"vertical-align: -12px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-263fd45c254c18d9499bc412292f3e17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c5ca20ad43730fc891b9d2a2757b968d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#121;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9a5b3c22bb39414b75fba2f7f523204b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a5997265c66b87439045a6e55e1895e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d3127367e70d7b513e073c420bf649a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#121;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d7bb26d3c9954af84f4dec11d7baa9fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#121;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"97\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-62860a11ef9e8308aab7711f4a34c432_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#120;&#43;&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"84\" style=\"vertical-align: -12px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bc1a9b27b39daccfa01205d055d7e96c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#45;&#121;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"113\" style=\"vertical-align: -12px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-81bf3fe4432aa807b30107962af3db18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#51;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0ff93eb9bb91e4a9bd6b32f826b8acd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#52;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6d784c787168d5f87e6eff6a45bff75b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#54;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b6d8b213589c98343ed7813237884ff4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<p id=\"fs-id1169596686274\">In the following exercises, graph each equation.<\/p>\n<ol class=\"twocolumn\" start=\"25\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8e36d35d8563f5053efd9935e88634f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-13491c682ce66c7951572caca92513bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"45\" style=\"vertical-align: -12px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fbf35c1c3a1b421219b33a19f4d3567e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"67\" style=\"vertical-align: -12px;\" \/><\/li>\n<\/ol>\n<p id=\"fs-id1169596635837\">In the following exercises, graph each pair of equations in the same rectangular coordinate system.<\/p>\n<ol class=\"twocolumn\" start=\"31\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4ecf689c13800069b252cefb0f1d5b07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a02de2a14f594681cc15523e4db5f5bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"70\" style=\"vertical-align: -12px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c92494e7fcc82c75879ff5a3fff0e080_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"58\" style=\"vertical-align: -12px;\" \/><\/li>\n<\/ol>\n<ol start=\"33\">\n<li>The Stonechilds rented a motor home for one week to go on vacation. It cost them &#36;594 plus &#36;0.32 per mile to rent the motor home, so the linear equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c47b47260655544884f05ecb6f4eac39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;&#57;&#52;&#43;&#48;&#46;&#51;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"123\" style=\"vertical-align: -4px;\" \/> gives the cost, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, for driving <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> miles. Calculate the rental cost for driving 400, 800, and 1200 miles, and then graph the line.<\/li>\n<\/ol>\n<h1>Answers<\/h1>\n<ol class=\"twocolumn\">\n<li>\n<ol type=\"A\">\n<li>yes; no<\/li>\n<li>no; no<\/li>\n<li>yes; yes<\/li>\n<li>yes; yes<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"A\">\n<li>yes; yes<\/li>\n<li>yes; yes<\/li>\n<li>yes; yes<\/li>\n<li>no; no<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<table style=\"border-collapse: collapse; width: 100%; height: 802px;\">\n<tbody>\n<tr style=\"height: 337px;\">\n<td style=\"height: 337px; width: 50.2516%;\">3.<\/p>\n<p><span id=\"fs-id1169594030487\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, negative 10), (negative 2, negative 7), (negative 1, negative 4), (0, negative 1), (1, 2), (2, 5), and (3, 8).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_201_img_new.jpg\" alt=\"Graph of the equation y = 3x \u2212 1.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p>&nbsp;<\/td>\n<td style=\"height: 337px; width: 49.7484%;\">4.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_203_img_new.jpg\" alt=\"Graph of the equation y = \u22123x + 3.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr style=\"height: 336px;\">\n<td style=\"height: 336px; width: 50.2516%;\">5.<\/p>\n<p><span id=\"fs-id1169594073542\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 10, negative 8), (negative 9, negative 7), (negative 8, negative 6), (negative 7, negative 5), (negative 6, negative 4), (negative 5, negative 3), (negative 4, negative 2), (negative 3, negative 1), (negative 2, 0), (negative 1, 1), (0, 2), (1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8), (7, 9), and (8, 10).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_205_img_new.jpg\" alt=\"Graph of the equation y = x + 2.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"height: 336px; width: 49.7484%;\">6.<\/p>\n<p><span id=\"fs-id1169594206333\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 10, 7), (negative 9, 6), (negative 8, 5), (negative 7, 4), (negative 6, 3), (negative 5, 2), (negative 4, 1), (negative 3, 0), (negative 2, negative 1), (negative 1, negative 2), (0, negative 3), (1, negative 4), (2, negative 5), (3, negative 6), (4, negative 7), (5, negative 8), (6, negative 9), and (7, negative 10).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_207_img_new.jpg\" alt=\"Graph of the equation y = \u2212x \u2212 3.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p>&nbsp;<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50.2516%; height: 16px;\">7.<\/p>\n<p><span id=\"fs-id1169594206416\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 5, negative 10), (negative 4, negative 8), (negative 3, negative 6), (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4), (3, 6), (4, 8), and (5, 10).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_209_img_new.jpg\" alt=\"Graph of the equation y = 2x.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.7484%; height: 16px;\">8.<\/p>\n<p><span id=\"fs-id1169596636216\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, 12), (negative 2, 8), (negative 1, 4), (0, 0), (1, negative 4), (2, negative 8), and (3, negative 12).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_211_img_new.jpg\" alt=\"Graph of the equation y = 3x.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50.2516%; height: 16px;\">9.<\/p>\n<p><span id=\"fs-id1169594077765\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 12, negative 4), (negative 10, negative 3), (negative 8, negative 2), (negative 6, negative 1), (negative 4, 0), (negative 2, 1), (0, 2), (2, 3), (4, 4), (6, 5), (8, 6), and (10, 7).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_213_img_new.jpg\" alt=\"Graph of the equation y = 1 half x + 2.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.7484%; height: 16px;\">10.<\/p>\n<p><span id=\"fs-id1169596662210\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, negative 9), (0, negative 5), (3, negative 1), (6, 3), and (9, 7).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_215_img_new.jpg\" alt=\"Graph of the equation y = 4 thirds x \u2212 5.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50.2516%; height: 16px;\">11.<\/p>\n<p><span id=\"fs-id1169596662303\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 10, 5), (negative 5, 3), (0, 1), (5, negative 1), and (10, negative 3).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_217_img_new.jpg\" alt=\"Graph of the equation y = \u2212 2 fifths x + 1.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.7484%; height: 16px;\">12.<\/p>\n<p><span id=\"fs-id1169596754110\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 6, 11), (negative 4, 8), (negative 2, 5), (0, 2), (2, negative 1), (4, negative 4), (6, negative 7), and (8, negative 10).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_219_img_new.jpg\" alt=\"Graph of the equation y = \u2212 3 halves x + 2.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50.2516%; height: 16px;\">13.<\/p>\n<p><span id=\"fs-id1169594073660\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, 10), (negative 3, 9), (negative 2, 8), (negative 1, 7), (0, 6), (1, 5), (2, 4), (3, 3), (4, 2), (5, 1), (6, 0), (7, negative 1), (8, negative 2), (9, negative 3), and (10, negative 4).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_221_img_new.jpg\" alt=\"Graph of the equation x + y = 6.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.7484%; height: 16px;\">14.<\/p>\n<p><span id=\"fs-id1169594150705\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 10, 7), (negative 9, 6), (negative 8, 5), (negative 7, 4), (negative 6, 3), (negative 5, 2), (negative 4, 1), (negative 3, 0), (negative 2, negative 1), (negative 1, negative 2), (0, negative 3), (1, negative 4), (2, negative 5), (3, negative 6), (4, negative 7), (5, negative 8), (6, negative 9), and (7, negative 10).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_223_img_new.jpg\" alt=\"Graph of the equation x + y = \u22123.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50.2516%; height: 16px;\">15.<\/p>\n<p><span id=\"fs-id1169594150788\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 8, negative 10), (negative 7, negative 9), (negative 6, negative 8), (negative 5, negative 7), (negative 4, negative 6), (negative 3, negative 5), (negative 2, negative 4), (negative 1, negative 3), (0, negative 2), (1, negative 1), (2, 0), (3, 1), (4, 2), (5, 3), (6, 4), (7, 5), (8, 6), (9, 7), and (10, 8).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_225_img_new.jpg\" alt=\"Graph of the equation x \u2212 y = 2.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.7484%; height: 16px;\">16.<\/p>\n<p><span id=\"fs-id1169594045893\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 9, negative 8), (negative 8, negative 7), (negative 7, negative 6), (negative 6, negative 5), (negative 5, negative 4), (negative 4, negative 3), (negative 3, negative 2), (negative 2, negative 1), (negative 1, 0), (0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9), and (9, 10).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_227_img_new.jpg\" alt=\"Graph of the equation x \u2212 y = \u22121.\" width=\"243\" height=\"249\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50.2516%; height: 16px;\">17.<\/p>\n<p><span id=\"fs-id1169596441600\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to -7. The equation 3 x plus y equals 7 is graphed.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_229_img_new.jpg\" alt=\"Graph of the equation 3x + y = 7.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.7484%; height: 16px;\">18.<\/p>\n<p><span id=\"fs-id1169596441683\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 5, 7), (negative 4, 5), (negative 3, 3), (negative 2, 1), (negative 1, negative 1), (0, negative 3), (1, negative 5), and (2, negative 7).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_231_img_new.jpg\" alt=\"Graph of the equation 2x + y = \u22123.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50.2516%; height: 16px;\">&nbsp;<\/p>\n<p>19.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_233_img_new.jpg\" alt=\"Graph of the equation 1 third x + y = 2.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p>&nbsp;<\/td>\n<td style=\"width: 49.7484%; height: 16px;\"><span id=\"fs-id1169596642392\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, 6), (negative 4, 5), (negative 2, 4), (0, 3), (2, 2), (4, 1), and (6, 0).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_268_img_new.jpg\" alt=\"Graph of the equation y = \u2212 1 half x + 3.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.2516%;\">21<\/p>\n<p><span id=\"fs-id1169594031029\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 3, 6), (0, 4), (3, 2), and (6, 0).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_237_img_new.jpg\" alt=\"Graph of the equation 2x + 3y = 12.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.7484%;\">22.<\/p>\n<p><span id=\"fs-id1169596766742\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 4, negative 6), (0, negative 3), (4, 0), and (8, 3).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_239_img_new.jpg\" alt=\"Graph of the equation 3x \u2212 4y = 12.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.2516%;\">23.<\/p>\n<p><span id=\"fs-id1169594056421\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, negative three halves), (negative 3, negative 1), (0, negative one half), (3, 0), and (6, one half).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_262_img_new.jpg\" alt=\"Graph of the equation x \u2212 6y = 3.\" width=\"229\" height=\"235\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.7484%;\">24.<\/p>\n<p><span id=\"fs-id1169594056507\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 2, 7), (0, 2), (2, negative 3), and (4, negative 8).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_264_img_new.jpg\" alt=\"Graph of the equation 3x + y = 2.\" width=\"229\" height=\"235\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.2516%;\">25.<\/p>\n<p><span id=\"fs-id1169594193072\" data-type=\"media\" data-alt=\"The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (4, 0), (4, 1), (4, 2) and all points with first coordinate 4.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_241_img_new.jpg\" alt=\"Graph of the equation x = 4. The resulting line is vertical.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.7484%;\">26.<\/p>\n<p><span id=\"fs-id1169596438663\" data-type=\"media\" data-alt=\"The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (negative 2, 0), (negative 2, 1), (negative 2, 2) and all points with first coordinate negative 2.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_243_img_new.jpg\" alt=\"Graph of the equation x = \u22122. The resulting line is vertical.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.2516%;\">27.<\/p>\n<p><span id=\"fs-id1169596438733\" data-type=\"media\" data-alt=\"The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The horizontal line goes through the points (0, 3), (1, 3), (2, 3) and all points with second coordinate 3.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_245_img_new.jpg\" alt=\"Graph of the line y = 3. The resulting line is horizontal.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.7484%;\">28.<\/p>\n<p><span id=\"fs-id1169594129360\" data-type=\"media\" data-alt=\"The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The horizontal line goes through the points (0, negative 5), (1, negative 5), (2, negative 5) and all points with second coordinate negative 5.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_247_img_new.jpg\" alt=\"Graph of the line y = \u22125. The resulting line is horizontal.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.2516%;\">29.<\/p>\n<p><span id=\"fs-id1169594129434\" data-type=\"media\" data-alt=\"The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (7\/3, 0), (7\/3, 1), (7\/3, 2) and all points with first coordinate 7\/3.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_249_img_new.jpg\" alt=\"Graph of the equation x = 7 thirds. The resulting line is vertical.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.7484%;\">30.<\/p>\n<p><span id=\"fs-id1169596635780\" data-type=\"media\" data-alt=\"The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The horizontal line goes through the points (0, negative 15\/4), (1, negative 15\/4), (2, negative 15\/4) and all points with second coordinate negative 15\/4.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_251_img_new.jpg\" alt=\"Graph of the equation y = \u2212 15 fourths. The resulting line is horizontal.\" width=\"228\" height=\"234\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.2516%;\">31.<\/p>\n<p><span id=\"fs-id1169594150826\" data-type=\"media\" data-alt=\"The figure shows a two straight lines drawn on the same x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. One line is a straight horizontal line going through the points (negative 4, 2) (0, 2), (4, 2), and all other points with second coordinate 2. The other line is a slanted line going through the points (negative 5, negative 10), (negative 4, negative 8), (negative 3, negative 6), (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4), (3, 6), (4, 8), and (5, 10).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_253_img_new.jpg\" alt=\"The equations y= 2x and y = 2 are graphed. The equation y = 2x is a slanted line while y = 2 is horizontal.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.7484%;\">32.<\/p>\n<p><span id=\"fs-id1169594150935\" data-type=\"media\" data-alt=\"The figure shows a two straight lines drawn on the same x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. One line is a straight horizontal line going through the points (negative 4, negative one half) (0, negative one half), (4, negative one half), and all other points with second coordinate negative one half. The other line is a slanted line going through the points (negative 10, 5), (negative 8, 4), (negative 6, 3), (negative 4, 2), (negative 2, 1), (0, 0), (1, negative 2), (2, negative 4), (3, negative 6), (4, negative 8), and (5, negative 10).\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_255_img_new.jpg\" alt=\"The equations y = \u2212 1 half x and y = \u2212 1 half are graphed. The equation y = \u2212 1 half x is a slanted line while y = \u2212 1 half is horizontal.\" width=\"243\" height=\"248\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.2516%;\">33. &#36;722, &#36;850, &#36;978<span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1169594149740\" data-type=\"media\" data-alt=\"The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from 0 to 1200 in increments of 100. The y-axis of the plane runs from 0 to 1000 in increments of 100. The straight line starts at the point (0, 594) and goes through the points (400, 722), (800, 850), and (1200, 978). The right end of the line has an arrow pointing up and to the right.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_02_257_img_new.jpg\" alt=\"Graph of the equation y = 594 + 0.32x.\" width=\"243\" height=\"205\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 49.7484%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"author":125,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-906","chapter","type-chapter","status-publish","hentry"],"part":777,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/906","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/users\/125"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/906\/revisions"}],"predecessor-version":[{"id":907,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/906\/revisions\/907"}],"part":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/parts\/777"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/906\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/media?parent=906"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapter-type?post=906"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/contributor?post=906"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/license?post=906"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}