{"id":4619,"date":"2017-06-07T18:53:31","date_gmt":"2017-06-07T18:53:31","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-graphing-linear-equations-in-different-forms\/"},"modified":"2017-08-16T02:56:46","modified_gmt":"2017-08-16T02:56:46","slug":"read-graphing-linear-equations-in-different-forms","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-graphing-linear-equations-in-different-forms\/","title":{"raw":"More Graphing Linear Equations With a Table and Vertical and Horizontal Lines","rendered":"More Graphing Linear Equations With a Table and Vertical and Horizontal Lines"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Graph Linear Equations in Different Forms\r\n<ul>\r\n \t<li>Solve for <em>y<\/em>, then graph a two-variable linear equation<\/li>\r\n \t<li>Graph horizontal and vertical lines<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Solve for <em>y<\/em>, then graph a linear equation<\/h2>\r\nThe linear equations we have graphed so far are in the form [latex]y=mx+b[\/latex] where <em>m<\/em> and <em>b<\/em> are real numbers. In this section we will graph linear equations that appear in different forms than we have seen.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nGraph the linear equation [latex]y+3x=5[\/latex].\r\n\r\n[reveal-answer q=\"61530\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"61530\"]First, solve [latex]y+3x=5[\/latex] for <em>y<\/em>, then the equation will look familiar and you can create a table of ordered pairs.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}y+3x-3x=5-3x\\\\y=5-3x\\end{array}[\/latex]<\/p>\r\nEvaluate [latex]y=5\u20133x[\/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><em>x <\/em>values<\/td>\r\n<td>[latex]5\u20133x[\/latex]<\/td>\r\n<td><em>y<\/em> values<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]0[\/latex]<\/td>\r\n<td>[latex]5\u20133(0)[\/latex]<\/td>\r\n<td>[latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]5\u20133(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]5\u20133(2)[\/latex]<\/td>\r\n<td>[latex]\u22121[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]5\u20133(3)[\/latex]<\/td>\r\n<td>[latex]\u22124[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nPlot the ordered pairs (shown below).\r\n<p style=\"text-align: center\">[latex](0,5)[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex](1,2)[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex](2,\u22121)[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex](3,\u22124)[\/latex]<\/p>\r\n<img class=\"aligncenter wp-image-1470\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185318\/Graphing-Linear-Equations-8.png\" alt=\"Graph showing the point (0,5), the point (1,2), the point (2,-1), and the point (3,-4).\" width=\"393\" height=\"303\" \/>\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-1471\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185322\/Graphing-Linear-Equations-9.png\" alt=\"Graphing Linear Equations (9)\" width=\"389\" height=\"300\" \/>[\/hidden-answer]\r\n\r\n<\/div>\r\nIn this video, you will see another example of graphing by using a table:\r\n\r\nhttps:\/\/youtu.be\/6yL3gfPbOt8\r\n<h2>Horizontal and Vertical Lines<\/h2>\r\nThe linear equations [latex]x=2[\/latex]\u00a0and [latex]y=\u22123[\/latex]\u00a0only have one variable in each of them. However, because these are linear equations, then they will graph on a coordinate plane just as the linear equations above do. Just think of the equation [latex]x=2[\/latex]\u00a0as [latex]x=0y+2[\/latex]\u00a0and think of [latex]y=\u22123[\/latex]\u00a0as [latex]y=0x\u20133[\/latex].\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nGraph [latex]y=\u22123[\/latex].\r\n\r\n[reveal-answer q=\"140758\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"140758\"]\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><em>x<\/em> values<\/td>\r\n<td>[latex]0x\u20133[\/latex]<\/td>\r\n<td><em>y<\/em> values<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]0[\/latex]<\/td>\r\n<td>[latex]0(0)\u20133[\/latex]<\/td>\r\n<td>[latex]\u22123[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]0(1)\u20133[\/latex]<\/td>\r\n<td>[latex]\u22123[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]0(2)\u20133[\/latex]<\/td>\r\n<td>[latex]\u22123[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]0(3)\u20133[\/latex]<\/td>\r\n<td>[latex]\u22123[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWrite [latex]y=\u22123[\/latex]\u00a0as [latex]y=0x\u20133[\/latex], and evaluate <em>y<\/em> when <em>x<\/em> has several values. Or just realize that [latex]y=\u22123[\/latex]\u00a0means every <em>y<\/em> value will be [latex]\u22123[\/latex], no matter what <em>x<\/em> is.\r\n<p style=\"text-align: center\">[latex](0,\u22123)[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex](1,\u22123)[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex](2,\u22123)[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex](3,\u22123)[\/latex]<\/p>\r\nPlot the ordered pairs (shown below).\r\n\r\n<img class=\"aligncenter wp-image-1473\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185326\/Graphing-Linear-Equations-10.png\" alt=\"Graph with the point (1,-3), the point (2,-3), and the point (3,-3).\" width=\"356\" height=\"274\" \/>\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-1474\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185329\/Graphing-Linear-Equations-11.png\" alt=\"Graphing Linear Equations (11)\" width=\"351\" height=\"270\" \/>Notice that [latex]y=\u22123[\/latex]\u00a0graphs as a horizontal line.[\/hidden-answer]\r\n\r\n<\/div>\r\n<p id=\"video3\">In this video, you will see how to graph both horizontal and vertical lines:<\/p>\r\nhttps:\/\/youtu.be\/2A2fhImjOBc","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Graph Linear Equations in Different Forms\n<ul>\n<li>Solve for <em>y<\/em>, then graph a two-variable linear equation<\/li>\n<li>Graph horizontal and vertical lines<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<h2>Solve for <em>y<\/em>, then graph a linear equation<\/h2>\n<p>The linear equations we have graphed so far are in the form [latex]y=mx+b[\/latex] where <em>m<\/em> and <em>b<\/em> are real numbers. In this section we will graph linear equations that appear in different forms than we have seen.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Graph the linear equation [latex]y+3x=5[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q61530\">Show Solution<\/span><\/p>\n<div id=\"q61530\" class=\"hidden-answer\" style=\"display: none\">First, solve [latex]y+3x=5[\/latex] for <em>y<\/em>, then the equation will look familiar and you can create a table of ordered pairs.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}y+3x-3x=5-3x\\\\y=5-3x\\end{array}[\/latex]<\/p>\n<p>Evaluate [latex]y=5\u20133x[\/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><em>x <\/em>values<\/td>\n<td>[latex]5\u20133x[\/latex]<\/td>\n<td><em>y<\/em> values<\/td>\n<\/tr>\n<tr>\n<td>[latex]0[\/latex]<\/td>\n<td>[latex]5\u20133(0)[\/latex]<\/td>\n<td>[latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]5\u20133(1)[\/latex]<\/td>\n<td>[latex]2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]5\u20133(2)[\/latex]<\/td>\n<td>[latex]\u22121[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]5\u20133(3)[\/latex]<\/td>\n<td>[latex]\u22124[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Plot the ordered pairs (shown below).<\/p>\n<p style=\"text-align: center\">[latex](0,5)[\/latex]<\/p>\n<p style=\"text-align: center\">[latex](1,2)[\/latex]<\/p>\n<p style=\"text-align: center\">[latex](2,\u22121)[\/latex]<\/p>\n<p style=\"text-align: center\">[latex](3,\u22124)[\/latex]<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1470\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185318\/Graphing-Linear-Equations-8.png\" alt=\"Graph showing the point (0,5), the point (1,2), the point (2,-1), and the point (3,-4).\" width=\"393\" height=\"303\" \/><\/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-1471\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185322\/Graphing-Linear-Equations-9.png\" alt=\"Graphing Linear Equations (9)\" width=\"389\" height=\"300\" \/><\/div>\n<\/div>\n<\/div>\n<p>In this video, you will see another example of graphing by using a table:<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex 3:  Graph a Linear Equation in Standard Form Using a Table of Values\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/6yL3gfPbOt8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Horizontal and Vertical Lines<\/h2>\n<p>The linear equations [latex]x=2[\/latex]\u00a0and [latex]y=\u22123[\/latex]\u00a0only have one variable in each of them. However, because these are linear equations, then they will graph on a coordinate plane just as the linear equations above do. Just think of the equation [latex]x=2[\/latex]\u00a0as [latex]x=0y+2[\/latex]\u00a0and think of [latex]y=\u22123[\/latex]\u00a0as [latex]y=0x\u20133[\/latex].<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Graph [latex]y=\u22123[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q140758\">Show Solution<\/span><\/p>\n<div id=\"q140758\" class=\"hidden-answer\" style=\"display: none\">\n<table>\n<tbody>\n<tr>\n<td><em>x<\/em> values<\/td>\n<td>[latex]0x\u20133[\/latex]<\/td>\n<td><em>y<\/em> values<\/td>\n<\/tr>\n<tr>\n<td>[latex]0[\/latex]<\/td>\n<td>[latex]0(0)\u20133[\/latex]<\/td>\n<td>[latex]\u22123[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]0(1)\u20133[\/latex]<\/td>\n<td>[latex]\u22123[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]0(2)\u20133[\/latex]<\/td>\n<td>[latex]\u22123[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]0(3)\u20133[\/latex]<\/td>\n<td>[latex]\u22123[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Write [latex]y=\u22123[\/latex]\u00a0as [latex]y=0x\u20133[\/latex], and evaluate <em>y<\/em> when <em>x<\/em> has several values. Or just realize that [latex]y=\u22123[\/latex]\u00a0means every <em>y<\/em> value will be [latex]\u22123[\/latex], no matter what <em>x<\/em> is.<\/p>\n<p style=\"text-align: center\">[latex](0,\u22123)[\/latex]<\/p>\n<p style=\"text-align: center\">[latex](1,\u22123)[\/latex]<\/p>\n<p style=\"text-align: center\">[latex](2,\u22123)[\/latex]<\/p>\n<p style=\"text-align: center\">[latex](3,\u22123)[\/latex]<\/p>\n<p>Plot the ordered pairs (shown below).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1473\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185326\/Graphing-Linear-Equations-10.png\" alt=\"Graph with the point (1,-3), the point (2,-3), and the point (3,-3).\" width=\"356\" height=\"274\" \/><\/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-1474\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185329\/Graphing-Linear-Equations-11.png\" alt=\"Graphing Linear Equations (11)\" width=\"351\" height=\"270\" \/>Notice that [latex]y=\u22123[\/latex]\u00a0graphs as a horizontal line.<\/div>\n<\/div>\n<\/div>\n<p id=\"video3\">In this video, you will see how to graph both horizontal and vertical lines:<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Graphing Horzontal and Vertical Lines (L8.6)\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/2A2fhImjOBc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\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-4619\">\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>Graphing Horizontal and Vertical Lines (L8.6). <strong>Authored by<\/strong>: mathispower4u. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/2A2fhImjOBc\">https:\/\/youtu.be\/2A2fhImjOBc<\/a>. <strong>License<\/strong>: <em>All Rights Reserved<\/em>. <strong>License Terms<\/strong>: Standard YouTube License<\/li><li>Ex 3: Graph a Linear Equation in Standard Form Using a Table of Values. <strong>Authored by<\/strong>: mathispower4u. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/6yL3gfPbOt8\">https:\/\/youtu.be\/6yL3gfPbOt8<\/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":17533,"menu_order":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"copyrighted_video\",\"description\":\"Graphing Horizontal and Vertical Lines (L8.6)\",\"author\":\"mathispower4u\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/2A2fhImjOBc\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"Standard YouTube License\"},{\"type\":\"copyrighted_video\",\"description\":\"Ex 3: Graph a Linear Equation in Standard Form Using a Table of Values\",\"author\":\"mathispower4u\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/6yL3gfPbOt8\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"Standard YouTube LIcense\"}]","CANDELA_OUTCOMES_GUID":"baba423a-eb54-42a9-abc8-cf62a233de5f","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4619","chapter","type-chapter","status-publish","hentry"],"part":4587,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters\/4619","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters\/4619\/revisions"}],"predecessor-version":[{"id":5074,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters\/4619\/revisions\/5074"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/parts\/4587"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters\/4619\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/media?parent=4619"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapter-type?post=4619"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/contributor?post=4619"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/license?post=4619"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}