{"id":3787,"date":"2020-02-08T19:40:50","date_gmt":"2020-02-08T19:40:50","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3787"},"modified":"2021-02-05T23:54:39","modified_gmt":"2021-02-05T23:54:39","slug":"identifying-the-intercepts-on-the-graph-of-a-line","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/identifying-the-intercepts-on-the-graph-of-a-line\/","title":{"raw":"Identifying the Intercepts on the Graph of a Line","rendered":"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 x and y-intercepts of a line given in equation form<\/li>\r\n \t<li>Identify the x and y-intercepts of a line given in graph form<\/li>\r\n<\/ul>\r\n<\/div>\r\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>\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<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\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]b[\/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 <em>x-intercept<\/em> of the line. The <strong>x-<\/strong> 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><em>x-<\/em> intercept and <em>y-<\/em> 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\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. To find the [latex]x\\text{-intercept,}[\/latex] let [latex]y=0[\/latex] and solve for [latex]x[\/latex]. To find the [latex]y\\text{-intercept}[\/latex], let [latex]x=0[\/latex] and solve for [latex]y[\/latex].<\/p>\r\n<p>In the following video, we provide another example of how to find the intercepts of a line from a graph.<\/p>\r\nhttps:\/\/youtu.be\/m5eQ_SjLVuw\r\n<div class=\"textbox shaded\">\r\n<h3>Find the <em>x<\/em> and <em>y<\/em> from the Equation of a Line<\/h3>\r\nUse the equation to find:\r\n\r\nthe <em>x-<\/em>intercept of the line, let [latex]y=0[\/latex] and solve for <em>x<\/em>.\r\n\r\nthe <em>y-<\/em>intercept of the line, let [latex]x=0[\/latex] and solve for <em>y<\/em>.\r\n<table id=\"eip-id1170322988395\" class=\"unnumbered-unstyled\" summary=\"...\">\r\n<thead>\r\n<tr>\r\n<th><strong>[latex]x[\/latex]<\/strong><\/th>\r\n<th><strong>[latex]y[\/latex]<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]0[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\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 x and y-intercepts of a line given in equation form<\/li>\n<li>Identify the x and y-intercepts of a line given in graph form<\/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<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<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]b[\/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 <em>x-intercept<\/em> of the line. The <strong>x-<\/strong> 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><em>x-<\/em> intercept and <em>y-<\/em> 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>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. To find the [latex]x\\text{-intercept,}[\/latex] let [latex]y=0[\/latex] and solve for [latex]x[\/latex]. To find the [latex]y\\text{-intercept}[\/latex], let [latex]x=0[\/latex] and solve for [latex]y[\/latex].<\/p>\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<div class=\"textbox shaded\">\n<h3>Find the <em>x<\/em> and <em>y<\/em> from the Equation of a Line<\/h3>\n<p>Use the equation to find:<\/p>\n<p>the <em>x-<\/em>intercept of the line, let [latex]y=0[\/latex] and solve for <em>x<\/em>.<\/p>\n<p>the <em>y-<\/em>intercept of the line, let [latex]x=0[\/latex] and solve for <em>y<\/em>.<\/p>\n<table id=\"eip-id1170322988395\" class=\"unnumbered-unstyled\" summary=\"...\">\n<thead>\n<tr>\n<th><strong>[latex]x[\/latex]<\/strong><\/th>\n<th><strong>[latex]y[\/latex]<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]0[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]0[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/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-3787\">\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>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":25777,"menu_order":7,"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 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(mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/vmaMT188ChA\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3787","chapter","type-chapter","status-web-only","hentry"],"part":1040,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3787","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3787\/revisions"}],"predecessor-version":[{"id":3788,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3787\/revisions\/3788"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/1040"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3787\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=3787"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=3787"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=3787"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=3787"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}