{"id":699,"date":"2016-06-01T20:49:14","date_gmt":"2016-06-01T20:49:14","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/?post_type=chapter&#038;p=699"},"modified":"2019-07-24T21:03:27","modified_gmt":"2019-07-24T21:03:27","slug":"read-quadrants-on-the-coordinate-plane","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/chapter\/read-quadrants-on-the-coordinate-plane\/","title":{"raw":"Graph Using Intercepts","rendered":"Graph Using Intercepts"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Recognize when an ordered pair is a <em>y<\/em>-intercept or an <em>x<\/em>-intercept<\/li>\r\n \t<li>Graph a linear equation using <em>x<\/em>\u00a0and <em>y<\/em>-intercepts<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2 id=\"Intercepts\">Intercepts<\/h2>\r\nThe intercepts of a line are the points where the line intersects 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\r\nThe straight line on the graph below intersects the two coordinate axes. The point where the line crosses the <i>x<\/i>-axis is called the <b><i>x<\/i>-intercept<\/b>. The <b><i>y<\/i>-intercept<\/b> 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\nThe <i>x<\/i>-intercept above is the point [latex](\u22122,0)[\/latex]. The <i>y<\/i>-intercept above is the point ([latex]0, 2[\/latex]).\r\n\r\nNotice that the <i>y<\/i>-intercept always occurs where [latex]x=0[\/latex], and the <i>x<\/i>-intercept always occurs where [latex]y=0[\/latex].\r\n\r\nTo find the <em>x<\/em>\u00a0and <em>y<\/em>-intercepts of a linear equation, you can substitute\u00a0[latex]0[\/latex] for <i>y<\/i> and for <i>x<\/i> respectively.\r\n\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<h3 id=\"Using Intercepts to Graph Lines\">Using Intercepts to Graph Lines<\/h3>\r\nYou can use intercepts to graph linear equations. Once you have found the two intercepts, draw a line through them.\r\n\r\nDo this with the equation [latex]3y+2x=6[\/latex]. You figured out that the intercepts of the line this equation represents are [latex](0,2)[\/latex] and [latex](3,0)[\/latex]. That is all you need to know.\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\/04064250\/image019-1.jpg\" alt=\"A line drawn through the points (0,2) and (3,0). The point (0,2) is labeled y-intercept and the point (3,0) is labeled x-intercept. The line is labeled 3y+2x=6.\" width=\"340\" height=\"344\" \/>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nGraph [latex]5y+3x=30[\/latex]\u00a0using the <em>x<\/em> and <em>y<\/em>-intercepts.\r\n\r\n[reveal-answer q=\"153435\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"153435\"]\r\n\r\nWhen an equation is in [latex]Ax+By=C[\/latex]\u00a0form, you can easily find the <i>x<\/i>- and <i>y<\/i>-intercepts and then graph.\r\n\r\nTo find the <i>y<\/i>-intercept, set [latex]x=0[\/latex]\u00a0and solve for <i>y<\/i>.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}5y+3x=30\\\\5y+3\\left(0\\right)=30\\\\5y+0=30\\\\5y=30\\\\y=\\,\\,\\,6\\\\y\\text{-intercept}\\,\\left(0,6\\right)\\end{array}[\/latex]<\/p>\r\nTo find the <i>x<\/i>-intercept, set [latex]y=0[\/latex] and solve for <i>x<\/i>.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}5y+3x=30\\\\5\\left(0\\right)+3x=30\\\\0+3x=30\\\\3x=30\\\\x=10\\\\x\\text{-intercept}\\left(10,0\\right)\\end{array}[\/latex]<\/p>\r\nThe graph can be seen below.\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\/04064251\/image020-1.jpg\" alt=\"\" width=\"425\" height=\"430\" \/>[\/hidden-answer]\r\n\r\n<\/div>\r\nhttps:\/\/youtu.be\/k8r-q_T6UFk\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nGraph [latex]y=2x-4[\/latex] using the <em>x<\/em> and <em>y<\/em>-intercepts.\r\n\r\n[reveal-answer q=\"476848\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"476848\"]\r\n\r\nFirst, find the <em>y<\/em>-intercept. Set <em>x<\/em> equal to zero and solve for <em>y<\/em>.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}y=2x-4\\\\y=2\\left(0\\right)-4\\\\y=0-4\\\\y=-4\\\\y\\text{-intercept}\\left(0,-4\\right)\\end{array}[\/latex]<\/p>\r\nTo find the <i>x<\/i>-intercept, set [latex]y=0[\/latex]\u00a0and solve for <i>x<\/i>.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}y=2x-4\\\\0=2x-4\\\\4=2x\\\\x=2\\\\x\\text{-intercept}\\left(2,0\\right)\\end{array}[\/latex]<\/p>\r\nThe graph can be seen below.\r\n\r\n<img class=\"size-medium wp-image-4163 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/545\/2016\/09\/16184439\/Screen-Shot-2016-09-16-at-11.42.53-AM-300x296.png\" alt=\"Line passing through (0,-4) and (2,0)\" width=\"300\" height=\"296\" \/>[\/hidden-answer]\r\n\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Recognize when an ordered pair is a <em>y<\/em>-intercept or an <em>x<\/em>-intercept<\/li>\n<li>Graph a linear equation using <em>x<\/em>\u00a0and <em>y<\/em>-intercepts<\/li>\n<\/ul>\n<\/div>\n<h2 id=\"Intercepts\">Intercepts<\/h2>\n<p>The intercepts of a line are the points where the line intersects 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<p>The straight line on the graph below intersects the two coordinate axes. The point where the line crosses the <i>x<\/i>-axis is called the <b><i>x<\/i>-intercept<\/b>. The <b><i>y<\/i>-intercept<\/b> 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>The <i>x<\/i>-intercept above is the point [latex](\u22122,0)[\/latex]. The <i>y<\/i>-intercept above is the point ([latex]0, 2[\/latex]).<\/p>\n<p>Notice that the <i>y<\/i>-intercept always occurs where [latex]x=0[\/latex], and the <i>x<\/i>-intercept always occurs where [latex]y=0[\/latex].<\/p>\n<p>To find the <em>x<\/em>\u00a0and <em>y<\/em>-intercepts of a linear equation, you can substitute\u00a0[latex]0[\/latex] for <i>y<\/i> and for <i>x<\/i> respectively.<\/p>\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<h3 id=\"Using Intercepts to Graph Lines\">Using Intercepts to Graph Lines<\/h3>\n<p>You can use intercepts to graph linear equations. Once you have found the two intercepts, draw a line through them.<\/p>\n<p>Do this with the equation [latex]3y+2x=6[\/latex]. You figured out that the intercepts of the line this equation represents are [latex](0,2)[\/latex] and [latex](3,0)[\/latex]. That is all you need to know.<\/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\/04064250\/image019-1.jpg\" alt=\"A line drawn through the points (0,2) and (3,0). The point (0,2) is labeled y-intercept and the point (3,0) is labeled x-intercept. The line is labeled 3y+2x=6.\" width=\"340\" height=\"344\" \/><\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Graph [latex]5y+3x=30[\/latex]\u00a0using the <em>x<\/em> and <em>y<\/em>-intercepts.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q153435\">Show Solution<\/span><\/p>\n<div id=\"q153435\" class=\"hidden-answer\" style=\"display: none\">\n<p>When an equation is in [latex]Ax+By=C[\/latex]\u00a0form, you can easily find the <i>x<\/i>&#8211; and <i>y<\/i>-intercepts and then graph.<\/p>\n<p>To find the <i>y<\/i>-intercept, set [latex]x=0[\/latex]\u00a0and solve for <i>y<\/i>.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}5y+3x=30\\\\5y+3\\left(0\\right)=30\\\\5y+0=30\\\\5y=30\\\\y=\\,\\,\\,6\\\\y\\text{-intercept}\\,\\left(0,6\\right)\\end{array}[\/latex]<\/p>\n<p>To find the <i>x<\/i>-intercept, set [latex]y=0[\/latex] and solve for <i>x<\/i>.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}5y+3x=30\\\\5\\left(0\\right)+3x=30\\\\0+3x=30\\\\3x=30\\\\x=10\\\\x\\text{-intercept}\\left(10,0\\right)\\end{array}[\/latex]<\/p>\n<p>The graph can be seen below.<\/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\/04064251\/image020-1.jpg\" alt=\"\" width=\"425\" height=\"430\" \/><\/div>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Graph Linear Equations Using Intercepts\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/k8r-q_T6UFk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Graph [latex]y=2x-4[\/latex] using the <em>x<\/em> and <em>y<\/em>-intercepts.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q476848\">Show Solution<\/span><\/p>\n<div id=\"q476848\" class=\"hidden-answer\" style=\"display: none\">\n<p>First, find the <em>y<\/em>-intercept. Set <em>x<\/em> equal to zero and solve for <em>y<\/em>.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}y=2x-4\\\\y=2\\left(0\\right)-4\\\\y=0-4\\\\y=-4\\\\y\\text{-intercept}\\left(0,-4\\right)\\end{array}[\/latex]<\/p>\n<p>To find the <i>x<\/i>-intercept, set [latex]y=0[\/latex]\u00a0and solve for <i>x<\/i>.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}y=2x-4\\\\0=2x-4\\\\4=2x\\\\x=2\\\\x\\text{-intercept}\\left(2,0\\right)\\end{array}[\/latex]<\/p>\n<p>The graph can be seen below.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-4163 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/545\/2016\/09\/16184439\/Screen-Shot-2016-09-16-at-11.42.53-AM-300x296.png\" alt=\"Line passing through (0,-4) and (2,0)\" width=\"300\" height=\"296\" \/><\/div>\n<\/div>\n<\/div>\n","protected":false},"author":21,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"1d30021b-8bf4-4003-85ec-8366ef8f0618","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-699","chapter","type-chapter","status-publish","hentry"],"part":473,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/699","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":9,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/699\/revisions"}],"predecessor-version":[{"id":5379,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/699\/revisions\/5379"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/parts\/473"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/699\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/media?parent=699"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=699"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/contributor?post=699"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/license?post=699"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}