{"id":781,"date":"2021-09-18T22:07:16","date_gmt":"2021-09-18T22:07:16","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/?post_type=chapter&#038;p=781"},"modified":"2021-12-06T22:55:12","modified_gmt":"2021-12-06T22:55:12","slug":"6-3-2-graph-vertical-and-horizontal-lines","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/chapter\/6-3-2-graph-vertical-and-horizontal-lines\/","title":{"raw":"6.3.2: Graphing Vertical and Horizontal Lines","rendered":"6.3.2: Graphing Vertical and Horizontal Lines"},"content":{"raw":"<div class=\"wrapper\">\r\n<div id=\"wrap\">\r\n<div id=\"content\" role=\"main\">\r\n<div id=\"post-136\" class=\"standard post-136 chapter type-chapter status-publish hentry\">\r\n<div class=\"entry-content\">\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nType your learning objectives here.\r\n<ul>\r\n \t<li>Graph a vertical line<\/li>\r\n \t<li>Give the equation of a vertical line<\/li>\r\n \t<li>Graph a horizontal line<\/li>\r\n \t<li>Give the equation of a horizontal line<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key words<\/h3>\r\nType your key takeaways here.\r\n<ul>\r\n \t<li><strong>vertical line<\/strong>: a line that runs in the same direction as the\u00a0<span style=\"text-align: center; font-size: 1em;\">[latex]y[\/latex]-axis<\/span><\/li>\r\n \t<li><strong>horizontal line<\/strong>: a line that runs in the same direction as the\u00a0<span style=\"text-align: center; font-size: 1em;\">[latex]x[\/latex]-axis<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Vertical and Horizontal Lines<\/h2>\r\nConsider the vertical line graphed in figure 1, and the solution table that goes with it.\r\n<div class=\"textbox\">\r\n<div id=\"post-136\" class=\"standard post-136 chapter type-chapter status-publish hentry\">\r\n<div class=\"entry-content\">\r\n\r\n&nbsp;\r\n\r\n<img class=\"alignleft wp-image-1949 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5676\/2021\/09\/02004444\/desmos-graph-34-300x300.png\" alt=\"x=2\" width=\"300\" height=\"300\" \/>\r\n<table style=\"border-collapse: collapse; width: 5.88145%; height: 220px;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<th class=\"border\" style=\"width: 1.5%; text-align: center;\">[latex]x[\/latex]<\/th>\r\n<th class=\"border\" style=\"width: 1.5%; text-align: center;\">[latex]y[\/latex]<\/th>\r\n<\/tr>\r\n<tr>\r\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">2<\/td>\r\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">-3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">2<\/td>\r\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">-1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">2<\/td>\r\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">2<\/td>\r\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">2<\/td>\r\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">\u00a03<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n<div id=\"post-136\" class=\"standard post-136 chapter type-chapter status-publish hentry\">\r\n<div class=\"entry-content\">\r\n\r\nNo matter the value of\u00a0[latex]y[\/latex],\u00a0[latex]x=2[\/latex]. So\u00a0[latex]x=2[\/latex] is the equation of the line.\r\n\r\nFigure 1.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"post-136\" class=\"standard post-136 chapter type-chapter status-publish hentry\">\r\n<div class=\"entry-content\">\r\n<div class=\"textbox shaded\">\r\n<h3>VERTICAL LINES<\/h3>\r\nThe equation of a\u00a0<strong><em>vertical line\u00a0<\/em><\/strong>is given as:\u00a0<span style=\"text-align: center; font-size: 1em;\">[latex]x=c[\/latex]\u00a0<\/span>where\u00a0<em>c <\/em>is a constant.\r\n\r\n<\/div>\r\nTo graph the equation on the coordinate plane, we need both [latex]x[\/latex] and [latex]y[\/latex] variables in the equation. Therefore, the equation of the vertical line in two variables is:\u00a0<span style=\"font-size: 1rem; text-align: center;\">[latex]x+0y=c[\/latex]\u00a0<\/span>where c is a constant.\r\n\r\nConsider the horizontal line graphed in figure 2, and the solution table that goes with it.\r\n<div class=\"textbox\">\r\n\r\n&nbsp;\r\n\r\n<img class=\"wp-image-1950 size-medium alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5676\/2021\/09\/02005242\/desmos-graph-35-300x300.png\" alt=\"y=3\" width=\"300\" height=\"300\" \/>\r\n<table style=\"border-collapse: collapse; width: 24.1743%; height: 225px;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<th class=\"border\" style=\"width: 50%; text-align: center;\">[latex]x[\/latex]<\/th>\r\n<th class=\"border\" style=\"width: 50%; text-align: center;\">[latex]y[\/latex]<\/th>\r\n<\/tr>\r\n<tr>\r\n<td class=\"border\" style=\"width: 50%; text-align: center;\">-3<\/td>\r\n<td class=\"border\" style=\"width: 50%; text-align: center;\">3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"border\" style=\"width: 50%; text-align: center;\">-1<\/td>\r\n<td class=\"border\" style=\"width: 50%; text-align: center;\">3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"border\" style=\"width: 50%; text-align: center;\">0<\/td>\r\n<td class=\"border\" style=\"width: 50%; text-align: center;\">3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"border\" style=\"width: 50%; text-align: center;\">2<\/td>\r\n<td class=\"border\" style=\"width: 50%; text-align: center;\">3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"border\" style=\"width: 50%; text-align: center;\">4<\/td>\r\n<td class=\"border\" style=\"width: 50%; text-align: center;\">\u00a03<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\nNo matter the\u00a0[latex]x[\/latex]-value, the\u00a0[latex]y[\/latex]-value is always 3. So the equation of the line is\u00a0[latex]y=3[\/latex].\r\n\r\nFigure 2.\r\n\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n<h3>HORIZONTAL LINES<\/h3>\r\nThe equation of a\u00a0<strong><em>horizontal line\u00a0<\/em><\/strong>is given as: [latex]y=c[\/latex] where\u00a0<em>c <\/em>is a constant.\r\n\r\n<\/div>\r\nTo graph the equation on the coordinate plane, we need both [latex]x[\/latex] and [latex]y[\/latex] variables in the equation. Therefore, the equation of the horizontal line in two variables is [latex]0x+y=c[\/latex].\r\n\r\nSuppose we want to graph a the lines with equations [latex]x+0y=-3[\/latex] and\u00a0[latex]0x+y=-2[\/latex].\r\n\r\nThe\u00a0following points satisfy the first equation: [latex]\\left(-3,-5\\right),\\left(-3,1\\right),\\left(-3,3\\right)[\/latex], and [latex]\\left(-3,5\\right)[\/latex]. We can plot the points. Notice that all of the [latex]x[\/latex]<em>-<\/em>coordinates are the same and we find a vertical line through [latex]x=-3[\/latex].\r\n\r\nThe\u00a0following points satisfy the second equation:\u00a0[latex]\\left(-2,-2\\right),\\left(0,-2\\right),\\left(3,-2\\right)[\/latex], and [latex]\\left(5,-2\\right)[\/latex]. The graph is a horizontal line through [latex]y=-2[\/latex]. Notice that all of the\u00a0[latex]y[\/latex]<em>-<\/em>coordinates are the same.\r\n<div class=\"wp-caption aligncenter\" style=\"width: 497px;\">\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/11185925\/CNX_CAT_Figure_02_02_003.jpg\" alt=\"Coordinate plane with the x-axis ranging from negative 7 to 4 and the y-axis ranging from negative 4 to 4. The function y = negative 2 and the line x = negative 3 are plotted.\" width=\"487\" height=\"367\" \/><i>x\u00a0<\/i>= \u22123 is a vertical line.\r\n<i>y\u00a0<\/i>= \u22122 is a horizontal line.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\nUse an online graphing tool to graph the following:\r\n<ol>\r\n \t<li>A horizontal line that passes through the point (-5,2)<\/li>\r\n \t<li>A vertical line that passes through the point (3,3)<\/li>\r\n<\/ol>\r\n<div class=\"wp-nocaption alignnone size-full wp-image-3370\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/College+Algebra\/calculator.html\" target=\"_blank\" rel=\"noopener\">\r\n<img class=\"alignnone size-full wp-image-3370\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/02\/13193222\/calculator.png\" sizes=\"(max-width: 251px) 100vw, 251px\" srcset=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/02\/13193222\/calculator.png 251w, https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/02\/13193222\/calculator-65x12.png 65w, https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/02\/13193222\/calculator-225x41.png 225w\" alt=\"\" width=\"251\" height=\"46\" \/>\r\n<\/a><\/div>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the equation of the line passing through the given points: [latex]\\left(1,-3\\right)[\/latex] and [latex]\\left(1,4\\right)[\/latex].\r\n<h4>Solution<\/h4>\r\nThe\u00a0[latex]x[\/latex]<em>-<\/em>coordinate of both points is 1. Therefore, we have a vertical line: [latex]x=1[\/latex].\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nFind the equation of the line passing through [latex]\\left(-5,2\\right)[\/latex] and [latex]\\left(2,2\\right)[\/latex].\r\n\r\n[reveal-answer q=\"404722\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"404722\"]\r\n\r\nHorizontal line: [latex]y=2[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n&nbsp;","rendered":"<div class=\"wrapper\">\n<div id=\"wrap\">\n<div id=\"content\" role=\"main\">\n<div id=\"post-136\" class=\"standard post-136 chapter type-chapter status-publish hentry\">\n<div class=\"entry-content\">\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>Type your learning objectives here.<\/p>\n<ul>\n<li>Graph a vertical line<\/li>\n<li>Give the equation of a vertical line<\/li>\n<li>Graph a horizontal line<\/li>\n<li>Give the equation of a horizontal line<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key words<\/h3>\n<p>Type your key takeaways here.<\/p>\n<ul>\n<li><strong>vertical line<\/strong>: a line that runs in the same direction as the\u00a0<span style=\"text-align: center; font-size: 1em;\">[latex]y[\/latex]-axis<\/span><\/li>\n<li><strong>horizontal line<\/strong>: a line that runs in the same direction as the\u00a0<span style=\"text-align: center; font-size: 1em;\">[latex]x[\/latex]-axis<\/span><\/li>\n<\/ul>\n<\/div>\n<h2>Vertical and Horizontal Lines<\/h2>\n<p>Consider the vertical line graphed in figure 1, and the solution table that goes with it.<\/p>\n<div class=\"textbox\">\n<div id=\"post-136\" class=\"standard post-136 chapter type-chapter status-publish hentry\">\n<div class=\"entry-content\">\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-1949 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5676\/2021\/09\/02004444\/desmos-graph-34-300x300.png\" alt=\"x=2\" width=\"300\" height=\"300\" \/><\/p>\n<table style=\"border-collapse: collapse; width: 5.88145%; height: 220px;\">\n<tbody>\n<tr>\n<th class=\"border\" style=\"width: 1.5%; text-align: center;\">[latex]x[\/latex]<\/th>\n<th class=\"border\" style=\"width: 1.5%; text-align: center;\">[latex]y[\/latex]<\/th>\n<\/tr>\n<tr>\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">2<\/td>\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">-3<\/td>\n<\/tr>\n<tr>\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">2<\/td>\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">-1<\/td>\n<\/tr>\n<tr>\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">2<\/td>\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">0<\/td>\n<\/tr>\n<tr>\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">2<\/td>\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">1<\/td>\n<\/tr>\n<tr>\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">2<\/td>\n<td class=\"border\" style=\"width: 1.5%; text-align: center;\">\u00a03<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div id=\"post-136\" class=\"standard post-136 chapter type-chapter status-publish hentry\">\n<div class=\"entry-content\">\n<p>No matter the value of\u00a0[latex]y[\/latex],\u00a0[latex]x=2[\/latex]. So\u00a0[latex]x=2[\/latex] is the equation of the line.<\/p>\n<p>Figure 1.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"post-136\" class=\"standard post-136 chapter type-chapter status-publish hentry\">\n<div class=\"entry-content\">\n<div class=\"textbox shaded\">\n<h3>VERTICAL LINES<\/h3>\n<p>The equation of a\u00a0<strong><em>vertical line\u00a0<\/em><\/strong>is given as:\u00a0<span style=\"text-align: center; font-size: 1em;\">[latex]x=c[\/latex]\u00a0<\/span>where\u00a0<em>c <\/em>is a constant.<\/p>\n<\/div>\n<p>To graph the equation on the coordinate plane, we need both [latex]x[\/latex] and [latex]y[\/latex] variables in the equation. Therefore, the equation of the vertical line in two variables is:\u00a0<span style=\"font-size: 1rem; text-align: center;\">[latex]x+0y=c[\/latex]\u00a0<\/span>where c is a constant.<\/p>\n<p>Consider the horizontal line graphed in figure 2, and the solution table that goes with it.<\/p>\n<div class=\"textbox\">\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1950 size-medium alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5676\/2021\/09\/02005242\/desmos-graph-35-300x300.png\" alt=\"y=3\" width=\"300\" height=\"300\" \/><\/p>\n<table style=\"border-collapse: collapse; width: 24.1743%; height: 225px;\">\n<tbody>\n<tr>\n<th class=\"border\" style=\"width: 50%; text-align: center;\">[latex]x[\/latex]<\/th>\n<th class=\"border\" style=\"width: 50%; text-align: center;\">[latex]y[\/latex]<\/th>\n<\/tr>\n<tr>\n<td class=\"border\" style=\"width: 50%; text-align: center;\">-3<\/td>\n<td class=\"border\" style=\"width: 50%; text-align: center;\">3<\/td>\n<\/tr>\n<tr>\n<td class=\"border\" style=\"width: 50%; text-align: center;\">-1<\/td>\n<td class=\"border\" style=\"width: 50%; text-align: center;\">3<\/td>\n<\/tr>\n<tr>\n<td class=\"border\" style=\"width: 50%; text-align: center;\">0<\/td>\n<td class=\"border\" style=\"width: 50%; text-align: center;\">3<\/td>\n<\/tr>\n<tr>\n<td class=\"border\" style=\"width: 50%; text-align: center;\">2<\/td>\n<td class=\"border\" style=\"width: 50%; text-align: center;\">3<\/td>\n<\/tr>\n<tr>\n<td class=\"border\" style=\"width: 50%; text-align: center;\">4<\/td>\n<td class=\"border\" style=\"width: 50%; text-align: center;\">\u00a03<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>No matter the\u00a0[latex]x[\/latex]-value, the\u00a0[latex]y[\/latex]-value is always 3. So the equation of the line is\u00a0[latex]y=3[\/latex].<\/p>\n<p>Figure 2.<\/p>\n<\/div>\n<div class=\"textbox shaded\">\n<h3>HORIZONTAL LINES<\/h3>\n<p>The equation of a\u00a0<strong><em>horizontal line\u00a0<\/em><\/strong>is given as: [latex]y=c[\/latex] where\u00a0<em>c <\/em>is a constant.<\/p>\n<\/div>\n<p>To graph the equation on the coordinate plane, we need both [latex]x[\/latex] and [latex]y[\/latex] variables in the equation. Therefore, the equation of the horizontal line in two variables is [latex]0x+y=c[\/latex].<\/p>\n<p>Suppose we want to graph a the lines with equations [latex]x+0y=-3[\/latex] and\u00a0[latex]0x+y=-2[\/latex].<\/p>\n<p>The\u00a0following points satisfy the first equation: [latex]\\left(-3,-5\\right),\\left(-3,1\\right),\\left(-3,3\\right)[\/latex], and [latex]\\left(-3,5\\right)[\/latex]. We can plot the points. Notice that all of the [latex]x[\/latex]<em>&#8211;<\/em>coordinates are the same and we find a vertical line through [latex]x=-3[\/latex].<\/p>\n<p>The\u00a0following points satisfy the second equation:\u00a0[latex]\\left(-2,-2\\right),\\left(0,-2\\right),\\left(3,-2\\right)[\/latex], and [latex]\\left(5,-2\\right)[\/latex]. The graph is a horizontal line through [latex]y=-2[\/latex]. Notice that all of the\u00a0[latex]y[\/latex]<em>&#8211;<\/em>coordinates are the same.<\/p>\n<div class=\"wp-caption aligncenter\" style=\"width: 497px;\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/11185925\/CNX_CAT_Figure_02_02_003.jpg\" alt=\"Coordinate plane with the x-axis ranging from negative 7 to 4 and the y-axis ranging from negative 4 to 4. The function y = negative 2 and the line x = negative 3 are plotted.\" width=\"487\" height=\"367\" \/><i>x\u00a0<\/i>= \u22123 is a vertical line.<br \/>\n<i>y\u00a0<\/i>= \u22122 is a horizontal line.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p>Use an online graphing tool to graph the following:<\/p>\n<ol>\n<li>A horizontal line that passes through the point (-5,2)<\/li>\n<li>A vertical line that passes through the point (3,3)<\/li>\n<\/ol>\n<div class=\"wp-nocaption alignnone size-full wp-image-3370\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/College+Algebra\/calculator.html\" target=\"_blank\" rel=\"noopener\"><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3370\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/02\/13193222\/calculator.png\" sizes=\"auto, (max-width: 251px) 100vw, 251px\" srcset=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/02\/13193222\/calculator.png 251w, https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/02\/13193222\/calculator-65x12.png 65w, https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/02\/13193222\/calculator-225x41.png 225w\" alt=\"\" width=\"251\" height=\"46\" \/><br \/>\n<\/a><\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find the equation of the line passing through the given points: [latex]\\left(1,-3\\right)[\/latex] and [latex]\\left(1,4\\right)[\/latex].<\/p>\n<h4>Solution<\/h4>\n<p>The\u00a0[latex]x[\/latex]<em>&#8211;<\/em>coordinate of both points is 1. Therefore, we have a vertical line: [latex]x=1[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Find the equation of the line passing through [latex]\\left(-5,2\\right)[\/latex] and [latex]\\left(2,2\\right)[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q404722\">Show Answer<\/span><\/p>\n<div id=\"q404722\" class=\"hidden-answer\" style=\"display: none\">\n<p>Horizontal line: [latex]y=2[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/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-781\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Figures 1 and 2.. <strong>Authored by<\/strong>: Hazel McKenna. <strong>Provided by<\/strong>: Utah Valley University. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: Abramson, Jay et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/li><li>Question ID 1719. <strong>Authored by<\/strong>: Barbara Goldner. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC- BY + GPL<\/li><li>Question ID 110942, 110946, 110951, 110952. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC- BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: OpenStax College Algebra. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/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":422608,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Abramson, Jay et 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