{"id":2367,"date":"2021-10-12T15:40:49","date_gmt":"2021-10-12T15:40:49","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2367"},"modified":"2022-04-23T00:10:18","modified_gmt":"2022-04-23T00:10:18","slug":"graphing-linear-equations-using-ordered-pairs","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/graphing-linear-equations-using-ordered-pairs\/","title":{"raw":"Graphing Linear Equations Using Ordered Pairs","rendered":"Graphing Linear Equations Using Ordered Pairs"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Complete a table of solutions for a linear equation<\/li>\r\n \t<li>Graph linear equations using ordered pairs<\/li>\r\n<\/ul>\r\n<\/div>\r\nBy graphing ordered pairs, we can interpret mathematical relationships. You can use a coordinate plane to plot points and map various relationships, such as the relationship between an object\u2019s distance and the elapsed time. Many mathematical relationships are linear relationships.\r\n<div>\r\n<h2 id=\"title1\">Plotting points to graph linear relationships<\/h2>\r\n<\/div>\r\nA linear relationship is a relationship between variables such that when plotted on a coordinate plane, the points lie on a line. Let\u2019s start by looking at a series of points in Quadrant I on the coordinate plane.\r\n\r\nLook at the five <b><strong>ordered pairs<\/strong><\/b> (and their <em>x<\/em>- and <em>y<\/em>-coordinates) below. Do you see any pattern in the location of the points? If this pattern continued, what other points could be on the line?\r\n\r\nYou probably identified that if this pattern continued the next ordered pair would be at [latex](5, 10)[\/latex]. This makes sense because the point [latex](5, 10)[\/latex] \u201clines up\u201d with the other points in the series\u2014it is literally on the same line as the others. Applying the same logic, you may identify that the ordered pairs [latex](6, 12)[\/latex] and [latex](7, 14)[\/latex] would also belong if this coordinate plane were larger; they, too, will line up with the other points.\r\n\r\nThese series of points can also be represented in a table. In the table below, the <em>x-<\/em>\u00a0and <em>y<\/em>-coordinates of each ordered pair on the graph is recorded.\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><b><strong><em>x<\/em><\/strong><\/b><b><strong>-coordinate<\/strong><\/b><\/td>\r\n<td><b><strong><em>y<\/em><\/strong><\/b><b><strong>-coordinate<\/strong><\/b><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]0[\/latex]<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nNotice that each <em>y<\/em>-coordinate is twice the corresponding <em>x<\/em>-value. All of these <em>x-<\/em>\u00a0and <em>y<\/em>-values follow the same pattern, and, when placed on a coordinate plane, they all line up.\r\n\r\n<img class=\"aligncenter wp-image-1458\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08205615\/Graphing-Linear-Equations-1.png\" alt=\"Graph with the point (0,0); the point (1,2); the point (2,4); the point (3,6); and the point (4,8).\" width=\"358\" height=\"276\" \/>\r\n\r\nOnce you know the pattern that relates the <em>x-<\/em> and <em>y-<\/em>values, you can find a <em>y<\/em>-value for any <em>x<\/em>-value that lies on the line. So if the rule of this pattern is that each <em>y<\/em>-coordinate is <em>twice<\/em> the corresponding <em>x<\/em>-value, then the ordered pairs [latex](1.5, 3), (2.5, 5)[\/latex], and [latex](3.5, 7)[\/latex] should all appear on the line too, correct? Look to see what happens.\r\n\r\n<img class=\"aligncenter wp-image-1459\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08210025\/Graphing-Linear-Equations-2.png\" alt=\"Graph with the point (0,0); the point (1,2); the point (1.5, 3); the point (2,4); the point (2.5, 5); the point (3,6); the point (3.5, 7); and the point (4,8).\" width=\"386\" height=\"297\" \/>\r\n\r\nIf you were to keep adding ordered pairs (<em>x<\/em>, <em>y<\/em>) where the <em>y<\/em>-value was twice the <em>x<\/em>-value, you would end up with a graph like this.\r\n\r\n<img class=\"aligncenter wp-image-1460\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08210231\/Graphing-Linear-Equations-3.png\" alt=\"A line drawn through the point (0,0); the point (1,2); the point (2,4); the point (3,6); and the point (4,8).\" width=\"386\" height=\"297\" \/>\r\n\r\nLook at how all of the points blend together to create a line. You can think of a line, then, as a collection of an infinite number of individual points that share the same mathematical relationship. In this case, the relationship is that the <em>y<\/em>-value is twice the <em>x<\/em>-value.\r\n\r\nThere are multiple ways to represent a linear relationship\u2014a table, a linear graph, and there is also a <b><strong>linear equation<\/strong><\/b>. A linear equation is an equation with two variables whose ordered pairs graph as a straight line.\r\n\r\nThere are several ways to create a graph from a linear equation. One way is to create a table of values for <em>x<\/em> and <em>y<\/em>, and then plot these ordered pairs on the coordinate plane. Two points are enough to determine a line. However, it\u2019s always a good idea to plot more than two points to avoid possible errors.\r\n\r\nThen you draw a line through the points to show all of the points that are on the line. The arrows at each end of the graph indicate that the line continues endlessly in both directions. Every point on this line is a solution to the linear equation.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nGraph the linear equation [latex]y=\u22121.5x[\/latex].\r\n\r\n[reveal-answer q=\"983342\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"983342\"]Evaluate [latex]y=\u22121.5x[\/latex]\u00a0for different values of <em>x<\/em>, and create a table of corresponding <em>x<\/em> and <em>y<\/em> values.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>[latex]x \\ values[\/latex]<\/td>\r\n<td>[latex]\u22121.5x[\/latex]<\/td>\r\n<td>[latex]y \\ values[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]0[\/latex]<\/td>\r\n<td>[latex]\u22121.5(0)[\/latex]<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]\u22121.5(2)[\/latex]<\/td>\r\n<td>[latex]\u22123[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]\u22121.5(4)[\/latex]<\/td>\r\n<td>[latex]\u22126[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]\u22121.5(6)[\/latex]<\/td>\r\n<td>[latex]\u22129[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSince the coefficient of <em>x<\/em> is [latex]\u22121.5[\/latex], it is convenient to choose multiples of [latex]2[\/latex] for <em>x<\/em>. This ensures that <em>y<\/em> is an integer, and makes the line easier to graph.\r\n\r\nConvert the table to ordered pairs. Then plot the ordered pairs.\r\n<p style=\"text-align: center;\">[latex](0,0)[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex](2,\u22123)[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex](4,\u22126)[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex](6,\u22129)[\/latex]<\/p>\r\nDraw a line through the points to indicate all of the points on the line.\r\n<h4>Answer\r\n<img class=\"aligncenter wp-image-1467\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08213504\/Graphing-Linear-Equations-52.png\" alt=\"A linear equation passes through the points (0, 0), (2, -3), (4, -6), and (6, -9).\" width=\"353\" height=\"271\" \/>[\/hidden-answer]<\/h4>\r\n<\/div>\r\n<h2>Graph the linear equation<\/h2>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nGraph the linear equation [latex]y=2x+3[\/latex].\r\n\r\n[reveal-answer q=\"834421\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"834421\"]Evaluate [latex]y=2x+3[\/latex]\u00a0for different values of <em>x<\/em>, and create a table of corresponding <em>x<\/em> and <em>y<\/em> values.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>[latex]x \\ values[\/latex]<\/td>\r\n<td>[latex]2x+3[\/latex]<\/td>\r\n<td>[latex]y \\ values[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]0[\/latex]<\/td>\r\n<td>[latex]2(0) + 3[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]2(1) + 3[\/latex]<\/td>\r\n<td>[latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]2(2) + 3[\/latex]<\/td>\r\n<td>[latex]7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]2(3) + 3[\/latex]<\/td>\r\n<td>[latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p style=\"text-align: center;\">[latex](0, 3)[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex](1, 5)[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex](2, 7)[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex](3, 9)[\/latex]<\/p>\r\nConvert the table to ordered pairs.\u00a0Plot the ordered pairs.\r\n\r\n<img class=\"aligncenter wp-image-1468\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08213653\/Graphing-Linear-Equations-6.png\" alt=\"Graph showing the point (0,3); the point (1,5); the point (2,7); and the point (3,9).\" width=\"317\" height=\"244\" \/>\r\n\r\nDraw a line through the points to indicate all of the points on the line.\r\n<h4>Answer<\/h4>\r\n<img class=\"aligncenter wp-image-1469\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08213931\/Graphing-Linear-Equations-7.png\" alt=\"Line drawn through the point (0,3); the point (1,5); the point (2,7); and the point (3,9). The line is labeled y=2x+3.\" width=\"275\" height=\"211\" \/>[\/hidden-answer]\r\n\r\n<\/div>\r\nhttps:\/\/youtu.be\/f5yvGPEWpvE\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]92754[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Complete a table of solutions for a linear equation<\/li>\n<li>Graph linear equations using ordered pairs<\/li>\n<\/ul>\n<\/div>\n<p>By graphing ordered pairs, we can interpret mathematical relationships. You can use a coordinate plane to plot points and map various relationships, such as the relationship between an object\u2019s distance and the elapsed time. Many mathematical relationships are linear relationships.<\/p>\n<div>\n<h2 id=\"title1\">Plotting points to graph linear relationships<\/h2>\n<\/div>\n<p>A linear relationship is a relationship between variables such that when plotted on a coordinate plane, the points lie on a line. Let\u2019s start by looking at a series of points in Quadrant I on the coordinate plane.<\/p>\n<p>Look at the five <b><strong>ordered pairs<\/strong><\/b> (and their <em>x<\/em>&#8211; and <em>y<\/em>-coordinates) below. Do you see any pattern in the location of the points? If this pattern continued, what other points could be on the line?<\/p>\n<p>You probably identified that if this pattern continued the next ordered pair would be at [latex](5, 10)[\/latex]. This makes sense because the point [latex](5, 10)[\/latex] \u201clines up\u201d with the other points in the series\u2014it is literally on the same line as the others. Applying the same logic, you may identify that the ordered pairs [latex](6, 12)[\/latex] and [latex](7, 14)[\/latex] would also belong if this coordinate plane were larger; they, too, will line up with the other points.<\/p>\n<p>These series of points can also be represented in a table. In the table below, the <em>x-<\/em>\u00a0and <em>y<\/em>-coordinates of each ordered pair on the graph is recorded.<\/p>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><b><strong><em>x<\/em><\/strong><\/b><b><strong>-coordinate<\/strong><\/b><\/td>\n<td><b><strong><em>y<\/em><\/strong><\/b><b><strong>-coordinate<\/strong><\/b><\/td>\n<\/tr>\n<tr>\n<td>[latex]0[\/latex]<\/td>\n<td>[latex]0[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]8[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>Notice that each <em>y<\/em>-coordinate is twice the corresponding <em>x<\/em>-value. All of these <em>x-<\/em>\u00a0and <em>y<\/em>-values follow the same pattern, and, when placed on a coordinate plane, they all line up.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1458\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08205615\/Graphing-Linear-Equations-1.png\" alt=\"Graph with the point (0,0); the point (1,2); the point (2,4); the point (3,6); and the point (4,8).\" width=\"358\" height=\"276\" \/><\/p>\n<p>Once you know the pattern that relates the <em>x-<\/em> and <em>y-<\/em>values, you can find a <em>y<\/em>-value for any <em>x<\/em>-value that lies on the line. So if the rule of this pattern is that each <em>y<\/em>-coordinate is <em>twice<\/em> the corresponding <em>x<\/em>-value, then the ordered pairs [latex](1.5, 3), (2.5, 5)[\/latex], and [latex](3.5, 7)[\/latex] should all appear on the line too, correct? Look to see what happens.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1459\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08210025\/Graphing-Linear-Equations-2.png\" alt=\"Graph with the point (0,0); the point (1,2); the point (1.5, 3); the point (2,4); the point (2.5, 5); the point (3,6); the point (3.5, 7); and the point (4,8).\" width=\"386\" height=\"297\" \/><\/p>\n<p>If you were to keep adding ordered pairs (<em>x<\/em>, <em>y<\/em>) where the <em>y<\/em>-value was twice the <em>x<\/em>-value, you would end up with a graph like this.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1460\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08210231\/Graphing-Linear-Equations-3.png\" alt=\"A line drawn through the point (0,0); the point (1,2); the point (2,4); the point (3,6); and the point (4,8).\" width=\"386\" height=\"297\" \/><\/p>\n<p>Look at how all of the points blend together to create a line. You can think of a line, then, as a collection of an infinite number of individual points that share the same mathematical relationship. In this case, the relationship is that the <em>y<\/em>-value is twice the <em>x<\/em>-value.<\/p>\n<p>There are multiple ways to represent a linear relationship\u2014a table, a linear graph, and there is also a <b><strong>linear equation<\/strong><\/b>. A linear equation is an equation with two variables whose ordered pairs graph as a straight line.<\/p>\n<p>There are several ways to create a graph from a linear equation. One way is to create a table of values for <em>x<\/em> and <em>y<\/em>, and then plot these ordered pairs on the coordinate plane. Two points are enough to determine a line. However, it\u2019s always a good idea to plot more than two points to avoid possible errors.<\/p>\n<p>Then you draw a line through the points to show all of the points that are on the line. The arrows at each end of the graph indicate that the line continues endlessly in both directions. Every point on this line is a solution to the linear equation.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Graph the linear equation [latex]y=\u22121.5x[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q983342\">Show Solution<\/span><\/p>\n<div id=\"q983342\" class=\"hidden-answer\" style=\"display: none\">Evaluate [latex]y=\u22121.5x[\/latex]\u00a0for different values of <em>x<\/em>, and create a table of corresponding <em>x<\/em> and <em>y<\/em> values.<\/p>\n<table>\n<tbody>\n<tr>\n<td>[latex]x \\ values[\/latex]<\/td>\n<td>[latex]\u22121.5x[\/latex]<\/td>\n<td>[latex]y \\ values[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]0[\/latex]<\/td>\n<td>[latex]\u22121.5(0)[\/latex]<\/td>\n<td>[latex]0[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]\u22121.5(2)[\/latex]<\/td>\n<td>[latex]\u22123[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]\u22121.5(4)[\/latex]<\/td>\n<td>[latex]\u22126[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]\u22121.5(6)[\/latex]<\/td>\n<td>[latex]\u22129[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Since the coefficient of <em>x<\/em> is [latex]\u22121.5[\/latex], it is convenient to choose multiples of [latex]2[\/latex] for <em>x<\/em>. This ensures that <em>y<\/em> is an integer, and makes the line easier to graph.<\/p>\n<p>Convert the table to ordered pairs. Then plot the ordered pairs.<\/p>\n<p style=\"text-align: center;\">[latex](0,0)[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex](2,\u22123)[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex](4,\u22126)[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex](6,\u22129)[\/latex]<\/p>\n<p>Draw a line through the points to indicate all of the points on the line.<\/p>\n<h4>Answer<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1467\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08213504\/Graphing-Linear-Equations-52.png\" alt=\"A linear equation passes through the points (0, 0), (2, -3), (4, -6), and (6, -9).\" width=\"353\" height=\"271\" \/><\/div>\n<\/div>\n<\/h4>\n<\/div>\n<h2>Graph the linear equation<\/h2>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Graph the linear equation [latex]y=2x+3[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q834421\">Show Solution<\/span><\/p>\n<div id=\"q834421\" class=\"hidden-answer\" style=\"display: none\">Evaluate [latex]y=2x+3[\/latex]\u00a0for different values of <em>x<\/em>, and create a table of corresponding <em>x<\/em> and <em>y<\/em> values.<\/p>\n<table>\n<tbody>\n<tr>\n<td>[latex]x \\ values[\/latex]<\/td>\n<td>[latex]2x+3[\/latex]<\/td>\n<td>[latex]y \\ values[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]0[\/latex]<\/td>\n<td>[latex]2(0) + 3[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]2(1) + 3[\/latex]<\/td>\n<td>[latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]2(2) + 3[\/latex]<\/td>\n<td>[latex]7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]2(3) + 3[\/latex]<\/td>\n<td>[latex]9[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\">[latex](0, 3)[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex](1, 5)[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex](2, 7)[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex](3, 9)[\/latex]<\/p>\n<p>Convert the table to ordered pairs.\u00a0Plot the ordered pairs.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1468\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08213653\/Graphing-Linear-Equations-6.png\" alt=\"Graph showing the point (0,3); the point (1,5); the point (2,7); and the point (3,9).\" width=\"317\" height=\"244\" \/><\/p>\n<p>Draw a line through the points to indicate all of the points on the line.<\/p>\n<h4>Answer<\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1469\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/08213931\/Graphing-Linear-Equations-7.png\" alt=\"Line drawn through the point (0,3); the point (1,5); the point (2,7); and the point (3,9). The line is labeled y=2x+3.\" width=\"275\" height=\"211\" \/><\/div>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Graph Basic Linear Equations by Completing a Table of Values\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/f5yvGPEWpvE?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm92754\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=92754&theme=oea&iframe_resize_id=ohm92754&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-2367\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">All rights reserved content<\/div><ul class=\"citation-list\"><li>Graph Basic Linear Equations by Completing a Table of Values. <strong>Authored by<\/strong>: mathispower4u. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/f5yvGPEWpvE\">https:\/\/youtu.be\/f5yvGPEWpvE<\/a>. <strong>License<\/strong>: <em>All Rights Reserved<\/em>. <strong>License Terms<\/strong>: Standard YouTube License<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"copyrighted_video\",\"description\":\"Graph Basic Linear Equations by Completing a Table of Values\",\"author\":\"mathispower4u\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/f5yvGPEWpvE\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"Standard YouTube License\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2367","chapter","type-chapter","status-publish","hentry"],"part":303,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2367","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2367\/revisions"}],"predecessor-version":[{"id":3963,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2367\/revisions\/3963"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/303"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2367\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=2367"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=2367"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=2367"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=2367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}