{"id":10682,"date":"2017-06-05T14:59:49","date_gmt":"2017-06-05T14:59:49","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10682"},"modified":"2020-10-22T09:16:50","modified_gmt":"2020-10-22T09:16:50","slug":"identifying-the-intercepts-on-the-graph-of-a-line","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/identifying-the-intercepts-on-the-graph-of-a-line\/","title":{"raw":"9.3.a - Identifying the Intercepts on the Graph of a Line","rendered":"9.3.a &#8211; Identifying the Intercepts on the Graph of a Line"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Identify the [latex]x[\/latex] and [latex]y[\/latex]-intercepts from the graph of a line<\/li>\r\n \t<li>Identify the [latex]x[\/latex] and [latex]y[\/latex]-intercepts from the equation of a line<\/li>\r\n<\/ul>\r\n<\/div>\r\nEvery linear equation has a unique line that represents all the solutions of the equation. When graphing a line by plotting points, each person who graphs the line can choose any three points, so two people graphing the line might use different sets of points.\r\n\r\nAt first glance, their two lines might appear different since they would have different points labeled. But if all the work was done correctly, the lines will be exactly the same line. One way to recognize that they are indeed the same line is to focus on where the line crosses the axes. Each of these points is called an intercept of the line.\r\n\r\nThe intercepts of a line are the points where the line intercepts, or crosses, the horizontal and vertical axes. To help you remember what \u201cintercept\u201d means, think about the word \u201cintersect.\u201d The two words sound alike and in this case mean the same thing.\r\n<div class=\"textbox shaded\">\r\n<h3>Intercepts of a Line<\/h3>\r\nEach of the points at which a line crosses the [latex]x\\text{-axis}[\/latex] and the [latex]y\\text{-axis}[\/latex] is called an intercept of the line.\r\n\r\n<\/div>\r\n<h2>Identify the [latex]x[\/latex]- and [latex]y[\/latex]- Intercepts From a Graph<\/h2>\r\nThe straight line on the graph below intercepts the two coordinate axes. The point where the line crosses the <i>x<\/i>-axis is called the [latex]x[\/latex]-intercept. The [latex]y[\/latex]-intercept is the point where the line crosses the <i>y<\/i>-axis.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/02\/04064249\/image018-1.jpg\" alt=\"A line going through two points. One point is on the x-axis and is labeled the x-intercept. The other point is on the y-axis and is labeled y-intercept.\" width=\"329\" height=\"320\" \/>\r\n\r\nIn the graph above, the x-intercept occurs when [latex]x=-2[\/latex] and the y-intercept occurs when [latex]y=2[\/latex].\u00a0 We typically express the intercepts by giving the ordered pair, so we say that the <i>x<\/i>-intercept above is at the point [latex](\u22122,0)[\/latex] and the <i>y<\/i>-intercept above is at the point [latex](0, 2)[\/latex].\r\n\r\nNotice that the intercept always occurs where [latex]x=0[\/latex], and the <i>x<\/i>-intercept always occurs where [latex]y=0[\/latex].\r\n\r\nLet\u2019s look at the graph of the lines shown below.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/25224410\/CNX_BMath_Figure_11_03_022_img.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through two labeled points, \" \/>\r\nFirst, notice where each of these lines crosses the <em>x<\/em>- axis:\r\n<table id=\"eip-59\" class=\"unnumbered-unstyled\" summary=\"...\">\r\n<thead>\r\n<tr>\r\n<th><strong>Figure:<\/strong><\/th>\r\n<th><strong>The line crosses the x-axis at:<\/strong><\/th>\r\n<th><strong>Ordered pair of this point<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]a[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex](3,0)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]b[\/latex]<\/td>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex](4,0)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]c[\/latex]<\/td>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex](5,0)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]d[\/latex]<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<td>[latex](0,0)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nDo you see a pattern?\r\n\r\nFor each row, the <em>y-<\/em> coordinate of the point where the line crosses the <em>x-<\/em> axis is zero. The point where the line crosses the <em>x-<\/em> axis has the form [latex]\\left(a,0\\right)[\/latex] ; and is called the x-intercept of the line. The x-intercept occurs when y is zero.\r\n\r\nNow, let's look at the points where these lines cross the y-axis.\r\n<table id=\"eip-196\" class=\"unnumbered-unstyled\" summary=\"...\">\r\n<thead>\r\n<tr>\r\n<th><strong>Figure:<\/strong><\/th>\r\n<th><strong>The line crosses the y-axis at:<\/strong><\/th>\r\n<th><strong>Ordered pair for this point<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]a[\/latex]<\/td>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex](0,6)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]b[\/latex]<\/td>\r\n<td>[latex]-3[\/latex]<\/td>\r\n<td>[latex](0,-3)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]c[\/latex]<\/td>\r\n<td>[latex]-5[\/latex]<\/td>\r\n<td>[latex](0,-5)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]d[\/latex]<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<td>[latex](0,0)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox shaded\">\r\n<h3>[latex]x[\/latex]-intercept and [latex]y[\/latex]-intercept of a line<\/h3>\r\nThe [latex]x\\text{-intercept}[\/latex] is the point, [latex]\\left(a,0\\right)[\/latex], where the graph crosses the [latex]x\\text{-axis}[\/latex]. The [latex]x\\text{-intercept}[\/latex] occurs when [latex]\\text{y}[\/latex] is zero.\r\nThe [latex]y\\text{-intercept}[\/latex] is the point, [latex]\\left(0,b\\right)[\/latex], where the graph crosses the [latex]y\\text{-axis}[\/latex]. The [latex]y\\text{-intercept}[\/latex] occurs when [latex]\\text{x}[\/latex] is zero.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFind the [latex]x\\text{- and }y\\text{-intercepts}[\/latex] of each line:\r\n<table id=\"eip-id1171459954315\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1. [latex]x+2y=4[\/latex]<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/25224413\/CNX_BMath_Figure_11_03_002.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through the points \" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2. [latex]3x-y=6[\/latex]<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/25224415\/CNX_BMath_Figure_11_03_003.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through the points \" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3. [latex]x+y=-5[\/latex]<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/25224416\/CNX_BMath_Figure_11_03_004.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through the points \" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSolution\r\n<table id=\"eip-id1172467163136\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The graph crosses the <em>x<\/em>-axis at the point [latex](4, 0)[\/latex].<\/td>\r\n<td>The <em>x<\/em>-intercept is [latex](4, 0)[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The graph crosses the <em>y<\/em>-axis at the point [latex](0, 2)[\/latex].<\/td>\r\n<td>The <em>y<\/em>-intercept is [latex](0, 2)[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1172467254989\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The graph crosses the <em>x<\/em>-axis at the point [latex](2, 0)[\/latex].<\/td>\r\n<td>The <em>x<\/em>-intercept is [latex](2, 0)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The graph crosses the <em>y<\/em>-axis at the point [latex](0, \u22126)[\/latex].<\/td>\r\n<td>The <em>y<\/em>-intercept is [latex](0, \u22126)[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168467276065\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The graph crosses the <em>x<\/em>-axis at the point [latex](\u22125, 0)[\/latex].<\/td>\r\n<td>The <em>x<\/em>-intercept is [latex](\u22125, 0)[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The graph crosses the <em>y<\/em>-axis at the point [latex](0, \u22125)[\/latex].<\/td>\r\n<td>The <em>y<\/em>-intercept is [latex](0, \u22125)[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146950[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video, we provide another example of how to find the intercepts of a line from a graph.\r\n\r\nhttps:\/\/youtu.be\/m5eQ_SjLVuw\r\n<h2>Find the Intercepts From an Equation of a Line<\/h2>\r\nRecognizing that the [latex]x\\text{-intercept}[\/latex] occurs when [latex]y[\/latex] is zero and that the [latex]y\\text{-intercept}[\/latex] occurs when [latex]x[\/latex] is zero gives us a method to find the intercepts of a line from its equation.\r\n<div class=\"textbox shaded\">\r\n<h3>How to Find the [latex]x[\/latex]-intercept and [latex]y[\/latex]-intercept Given An Equation of a line<\/h3>\r\nTo find the [latex]x\\text{-intercept,}[\/latex] let [latex]y=0[\/latex] and solve for [latex]x[\/latex].\r\n\r\nTo find the [latex]y\\text{-intercept}[\/latex], let [latex]x=0[\/latex] and solve for [latex]y[\/latex].\r\n\r\n<\/div>\r\nFor example, the linear equation [latex]3y+2x=6[\/latex]\u00a0has an <i>x<\/i> intercept when [latex]y=0[\/latex], so [latex]3\\left(0\\right)+2x=6[\/latex].\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}2x=6\\\\x=3\\end{array}[\/latex]<\/p>\r\nThe <em>x<\/em>-intercept is [latex](3,0)[\/latex].\r\n\r\nLikewise the <i>y<\/i>-intercept occurs when [latex]x=0[\/latex].\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}3y+2\\left(0\\right)=6\\\\3y=6\\\\y=2\\end{array}[\/latex]<\/p>\r\nThe <i>y<\/i>-intercept is [latex](0,2)[\/latex].\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFind the intercepts of [latex]2x+y=6[\/latex]\r\n\r\nWe'll fill in the table below.\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/25224421\/CNX_BMath_Figure_11_03_023_img.png\" alt=\"...\" \/>\r\nTo find the x- intercept, let [latex]y=0[\/latex] :\r\n<table id=\"eip-id1172465967137\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]2x+y=6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]0[\/latex] for <em>y<\/em>.<\/td>\r\n<td>[latex]2x+\\color{red}{0}=6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]2x=6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide by [latex]2[\/latex].<\/td>\r\n<td>[latex]x=3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The <em>x<\/em>-intercept is [latex](3, 0)[\/latex].<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nTo find the y- intercept, let [latex]x=0[\/latex] :\r\n<table id=\"eip-id1172467250988\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]2x+y=6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]0[\/latex] for <em>x<\/em>.<\/td>\r\n<td>[latex]2\\cdot\\color{red}{0}+y=6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]0+y=6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]y=6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The <em>y<\/em>-intercept is [latex](0, 6)[\/latex].<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/25224430\/CNX_BMath_Figure_11_03_026_img.png\" alt=\"...\" \/>\r\nThe intercepts are the points [latex]\\left(3,0\\right)[\/latex] and [latex]\\left(0,6\\right)[\/latex] .\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146996[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFind the intercepts of [latex]4x - 3y=12[\/latex]\r\n[reveal-answer q=\"219115\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"219115\"]\r\n\r\nSolution\r\nTo find the [latex]x\\text{-intercept,}[\/latex] let [latex]y=0[\/latex].\r\n<table id=\"eip-id1168466092915\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]4x - 3y=12[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]0[\/latex] for [latex]y[\/latex].<\/td>\r\n<td>[latex]4x - 3\\cdot 0=12[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]4x - 0=12[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td>[latex]4x=12[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide by [latex]4[\/latex].<\/td>\r\n<td>[latex]x=3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe [latex]x\\text{-intercept}[\/latex] is [latex]\\left(3,0\\right)[\/latex].\r\nTo find the [latex]y\\text{-intercept}[\/latex], let [latex]x=0[\/latex].\r\n<table id=\"eip-id1168468289016\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]4x - 3y=12[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]0[\/latex] for [latex]x[\/latex].<\/td>\r\n<td>[latex]4\\cdot 0 - 3y=12[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]0 - 3y=12[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]-3y=12[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide by [latex]\u22123[\/latex].<\/td>\r\n<td>[latex]y=-4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe [latex]y\\text{-intercept}[\/latex] is [latex]\\left(0,-4\\right)[\/latex].\r\nThe intercepts are the points [latex]\\left(-3,0\\right)[\/latex] and [latex]\\left(0,-4\\right)[\/latex].\r\n<table id=\"fs-id1722979\" class=\"unnumbered\" summary=\"This table it titled 4 x - 3 y = 12. It has 2 rows and 2columns. Under the first column are the values 3 and 0. Under the second column are the values 0 and -4.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th colspan=\"2\">[latex]4x - 3y=12[\/latex]<\/th>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<th>x<\/th>\r\n<th>y<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]0[\/latex]<\/td>\r\n<td>[latex]-4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146997[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following example we show you how to find the intercepts of a line given in a different form than the examples above.\r\n\r\nhttps:\/\/youtu.be\/vmaMT188ChA","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Identify the [latex]x[\/latex] and [latex]y[\/latex]-intercepts from the graph of a line<\/li>\n<li>Identify the [latex]x[\/latex] and [latex]y[\/latex]-intercepts from the equation of a line<\/li>\n<\/ul>\n<\/div>\n<p>Every linear equation has a unique line that represents all the solutions of the equation. When graphing a line by plotting points, each person who graphs the line can choose any three points, so two people graphing the line might use different sets of points.<\/p>\n<p>At first glance, their two lines might appear different since they would have different points labeled. But if all the work was done correctly, the lines will be exactly the same line. One way to recognize that they are indeed the same line is to focus on where the line crosses the axes. Each of these points is called an intercept of the line.<\/p>\n<p>The intercepts of a line are the points where the line intercepts, or crosses, the horizontal and vertical axes. To help you remember what \u201cintercept\u201d means, think about the word \u201cintersect.\u201d The two words sound alike and in this case mean the same thing.<\/p>\n<div class=\"textbox shaded\">\n<h3>Intercepts of a Line<\/h3>\n<p>Each of the points at which a line crosses the [latex]x\\text{-axis}[\/latex] and the [latex]y\\text{-axis}[\/latex] is called an intercept of the line.<\/p>\n<\/div>\n<h2>Identify the [latex]x[\/latex]&#8211; and [latex]y[\/latex]&#8211; Intercepts From a Graph<\/h2>\n<p>The straight line on the graph below intercepts the two coordinate axes. The point where the line crosses the <i>x<\/i>-axis is called the [latex]x[\/latex]-intercept. The [latex]y[\/latex]-intercept is the point where the line crosses the <i>y<\/i>-axis.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/02\/04064249\/image018-1.jpg\" alt=\"A line going through two points. One point is on the x-axis and is labeled the x-intercept. The other point is on the y-axis and is labeled y-intercept.\" width=\"329\" height=\"320\" \/><\/p>\n<p>In the graph above, the x-intercept occurs when [latex]x=-2[\/latex] and the y-intercept occurs when [latex]y=2[\/latex].\u00a0 We typically express the intercepts by giving the ordered pair, so we say that the <i>x<\/i>-intercept above is at the point [latex](\u22122,0)[\/latex] and the <i>y<\/i>-intercept above is at the point [latex](0, 2)[\/latex].<\/p>\n<p>Notice that the intercept always occurs where [latex]x=0[\/latex], and the <i>x<\/i>-intercept always occurs where [latex]y=0[\/latex].<\/p>\n<p>Let\u2019s look at the graph of the lines shown below.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/25224410\/CNX_BMath_Figure_11_03_022_img.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through two labeled points,\" \/><br \/>\nFirst, notice where each of these lines crosses the <em>x<\/em>&#8211; axis:<\/p>\n<table id=\"eip-59\" class=\"unnumbered-unstyled\" summary=\"...\">\n<thead>\n<tr>\n<th><strong>Figure:<\/strong><\/th>\n<th><strong>The line crosses the x-axis at:<\/strong><\/th>\n<th><strong>Ordered pair of this point<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]a[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex](3,0)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]b[\/latex]<\/td>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex](4,0)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]c[\/latex]<\/td>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex](5,0)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]d[\/latex]<\/td>\n<td>[latex]0[\/latex]<\/td>\n<td>[latex](0,0)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Do you see a pattern?<\/p>\n<p>For each row, the <em>y-<\/em> coordinate of the point where the line crosses the <em>x-<\/em> axis is zero. The point where the line crosses the <em>x-<\/em> axis has the form [latex]\\left(a,0\\right)[\/latex] ; and is called the x-intercept of the line. The x-intercept occurs when y is zero.<\/p>\n<p>Now, let&#8217;s look at the points where these lines cross the y-axis.<\/p>\n<table id=\"eip-196\" class=\"unnumbered-unstyled\" summary=\"...\">\n<thead>\n<tr>\n<th><strong>Figure:<\/strong><\/th>\n<th><strong>The line crosses the y-axis at:<\/strong><\/th>\n<th><strong>Ordered pair for this point<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]a[\/latex]<\/td>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex](0,6)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]b[\/latex]<\/td>\n<td>[latex]-3[\/latex]<\/td>\n<td>[latex](0,-3)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]c[\/latex]<\/td>\n<td>[latex]-5[\/latex]<\/td>\n<td>[latex](0,-5)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]d[\/latex]<\/td>\n<td>[latex]0[\/latex]<\/td>\n<td>[latex](0,0)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox shaded\">\n<h3>[latex]x[\/latex]-intercept and [latex]y[\/latex]-intercept of a line<\/h3>\n<p>The [latex]x\\text{-intercept}[\/latex] is the point, [latex]\\left(a,0\\right)[\/latex], where the graph crosses the [latex]x\\text{-axis}[\/latex]. The [latex]x\\text{-intercept}[\/latex] occurs when [latex]\\text{y}[\/latex] is zero.<br \/>\nThe [latex]y\\text{-intercept}[\/latex] is the point, [latex]\\left(0,b\\right)[\/latex], where the graph crosses the [latex]y\\text{-axis}[\/latex]. The [latex]y\\text{-intercept}[\/latex] occurs when [latex]\\text{x}[\/latex] is zero.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Find the [latex]x\\text{- and }y\\text{-intercepts}[\/latex] of each line:<\/p>\n<table id=\"eip-id1171459954315\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1. [latex]x+2y=4[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/25224413\/CNX_BMath_Figure_11_03_002.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through the points\" \/><\/td>\n<\/tr>\n<tr>\n<td>2. [latex]3x-y=6[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/25224415\/CNX_BMath_Figure_11_03_003.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through the points\" \/><\/td>\n<\/tr>\n<tr>\n<td>3. [latex]x+y=-5[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/25224416\/CNX_BMath_Figure_11_03_004.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through the points\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Solution<\/p>\n<table id=\"eip-id1172467163136\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The graph crosses the <em>x<\/em>-axis at the point [latex](4, 0)[\/latex].<\/td>\n<td>The <em>x<\/em>-intercept is [latex](4, 0)[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>The graph crosses the <em>y<\/em>-axis at the point [latex](0, 2)[\/latex].<\/td>\n<td>The <em>y<\/em>-intercept is [latex](0, 2)[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1172467254989\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The graph crosses the <em>x<\/em>-axis at the point [latex](2, 0)[\/latex].<\/td>\n<td>The <em>x<\/em>-intercept is [latex](2, 0)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The graph crosses the <em>y<\/em>-axis at the point [latex](0, \u22126)[\/latex].<\/td>\n<td>The <em>y<\/em>-intercept is [latex](0, \u22126)[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467276065\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The graph crosses the <em>x<\/em>-axis at the point [latex](\u22125, 0)[\/latex].<\/td>\n<td>The <em>x<\/em>-intercept is [latex](\u22125, 0)[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>The graph crosses the <em>y<\/em>-axis at the point [latex](0, \u22125)[\/latex].<\/td>\n<td>The <em>y<\/em>-intercept is [latex](0, \u22125)[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146950\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146950&theme=oea&iframe_resize_id=ohm146950&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video, we provide another example of how to find the intercepts of a line from a graph.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  State the X and Y Intercepts Given the Graph of a Line\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/m5eQ_SjLVuw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Find the Intercepts From an Equation of a Line<\/h2>\n<p>Recognizing that the [latex]x\\text{-intercept}[\/latex] occurs when [latex]y[\/latex] is zero and that the [latex]y\\text{-intercept}[\/latex] occurs when [latex]x[\/latex] is zero gives us a method to find the intercepts of a line from its equation.<\/p>\n<div class=\"textbox shaded\">\n<h3>How to Find the [latex]x[\/latex]-intercept and [latex]y[\/latex]-intercept Given An Equation of a line<\/h3>\n<p>To find the [latex]x\\text{-intercept,}[\/latex] let [latex]y=0[\/latex] and solve for [latex]x[\/latex].<\/p>\n<p>To find the [latex]y\\text{-intercept}[\/latex], let [latex]x=0[\/latex] and solve for [latex]y[\/latex].<\/p>\n<\/div>\n<p>For example, the linear equation [latex]3y+2x=6[\/latex]\u00a0has an <i>x<\/i> intercept when [latex]y=0[\/latex], so [latex]3\\left(0\\right)+2x=6[\/latex].<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}2x=6\\\\x=3\\end{array}[\/latex]<\/p>\n<p>The <em>x<\/em>-intercept is [latex](3,0)[\/latex].<\/p>\n<p>Likewise the <i>y<\/i>-intercept occurs when [latex]x=0[\/latex].<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}3y+2\\left(0\\right)=6\\\\3y=6\\\\y=2\\end{array}[\/latex]<\/p>\n<p>The <i>y<\/i>-intercept is [latex](0,2)[\/latex].<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Find the intercepts of [latex]2x+y=6[\/latex]<\/p>\n<p>We&#8217;ll fill in the table below.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/25224421\/CNX_BMath_Figure_11_03_023_img.png\" alt=\"...\" \/><br \/>\nTo find the x- intercept, let [latex]y=0[\/latex] :<\/p>\n<table id=\"eip-id1172465967137\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]2x+y=6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]0[\/latex] for <em>y<\/em>.<\/td>\n<td>[latex]2x+\\color{red}{0}=6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]2x=6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide by [latex]2[\/latex].<\/td>\n<td>[latex]x=3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The <em>x<\/em>-intercept is [latex](3, 0)[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>To find the y- intercept, let [latex]x=0[\/latex] :<\/p>\n<table id=\"eip-id1172467250988\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]2x+y=6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]0[\/latex] for <em>x<\/em>.<\/td>\n<td>[latex]2\\cdot\\color{red}{0}+y=6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]0+y=6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]y=6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The <em>y<\/em>-intercept is [latex](0, 6)[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/25224430\/CNX_BMath_Figure_11_03_026_img.png\" alt=\"...\" \/><br \/>\nThe intercepts are the points [latex]\\left(3,0\\right)[\/latex] and [latex]\\left(0,6\\right)[\/latex] .<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146996\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146996&theme=oea&iframe_resize_id=ohm146996&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Find the intercepts of [latex]4x - 3y=12[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q219115\">Show Solution<\/span><\/p>\n<div id=\"q219115\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nTo find the [latex]x\\text{-intercept,}[\/latex] let [latex]y=0[\/latex].<\/p>\n<table id=\"eip-id1168466092915\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]4x - 3y=12[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]0[\/latex] for [latex]y[\/latex].<\/td>\n<td>[latex]4x - 3\\cdot 0=12[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]4x - 0=12[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>[latex]4x=12[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide by [latex]4[\/latex].<\/td>\n<td>[latex]x=3[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The [latex]x\\text{-intercept}[\/latex] is [latex]\\left(3,0\\right)[\/latex].<br \/>\nTo find the [latex]y\\text{-intercept}[\/latex], let [latex]x=0[\/latex].<\/p>\n<table id=\"eip-id1168468289016\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]4x - 3y=12[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]0[\/latex] for [latex]x[\/latex].<\/td>\n<td>[latex]4\\cdot 0 - 3y=12[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]0 - 3y=12[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-3y=12[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide by [latex]\u22123[\/latex].<\/td>\n<td>[latex]y=-4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The [latex]y\\text{-intercept}[\/latex] is [latex]\\left(0,-4\\right)[\/latex].<br \/>\nThe intercepts are the points [latex]\\left(-3,0\\right)[\/latex] and [latex]\\left(0,-4\\right)[\/latex].<\/p>\n<table id=\"fs-id1722979\" class=\"unnumbered\" summary=\"This table it titled 4 x - 3 y = 12. It has 2 rows and 2columns. Under the first column are the values 3 and 0. Under the second column are the values 0 and -4.\">\n<thead>\n<tr valign=\"top\">\n<th colspan=\"2\">[latex]4x - 3y=12[\/latex]<\/th>\n<\/tr>\n<tr valign=\"top\">\n<th>x<\/th>\n<th>y<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]0[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]0[\/latex]<\/td>\n<td>[latex]-4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146997\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146997&theme=oea&iframe_resize_id=ohm146997&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following example we show you how to find the intercepts of a line given in a different form than the examples above.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex:  Determine the x and y Intercepts of a Linear Equation in Slope Intercept Form\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/vmaMT188ChA?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-10682\">\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>Question ID 146997, 146996, 146950. <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><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: State the X and Y Intercepts Given the Graph of a Line. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/m5eQ_SjLVuw\">https:\/\/youtu.be\/m5eQ_SjLVuw<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Ex: Determine the x and y Intercepts of a Linear Equation in Slope Intercept Form. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/vmaMT188ChA\">https:\/\/youtu.be\/vmaMT188ChA<\/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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <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\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/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":13,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146997, 146996, 146950\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: State the X and Y Intercepts Given the Graph of a Line\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/m5eQ_SjLVuw\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Determine the x and y Intercepts of a Linear Equation in Slope Intercept Form\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/vmaMT188ChA\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"0a4cf7b473d74cb5b51e82292e049f41, 538d3853a1d94e6ab24bee558d88960f, f4501dc69ac34ca2a70716f9ff5f0cbe","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-10682","chapter","type-chapter","status-publish","hentry"],"part":8524,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10682","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":21,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10682\/revisions"}],"predecessor-version":[{"id":20338,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10682\/revisions\/20338"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/8524"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10682\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/media?parent=10682"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=10682"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=10682"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/license?post=10682"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}