{"id":4623,"date":"2017-06-07T18:53:37","date_gmt":"2017-06-07T18:53:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-intercepts\/"},"modified":"2017-08-16T02:58:42","modified_gmt":"2017-08-16T02:58:42","slug":"read-intercepts","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-intercepts\/","title":{"raw":"Graphing Linear Equations Using Intercepts","rendered":"Graphing Linear Equations Using Intercepts"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Graph an Equation Using Intercepts\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>- and <em>y<\/em>-intercepts<\/li>\r\n<\/ul>\r\n<\/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 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\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 <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\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185331\/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 (0, 2).\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>- and <em>y<\/em>-intercepts of a linear equation, you can substitute 0 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<h2><span style=\"color: #4588bf\">Using Intercepts to Graph Lines<\/span><\/h2>\r\nYou can use intercepts to graph linear equations. Once you have found the two intercepts, draw a line through them.\r\n\r\nLet\u2019s do it 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\u2019s all you need to know.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185333\/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\"]When 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<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>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\\\\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\nTo find the <i>x<\/i>-intercept, set [latex]y=0[\/latex] and solve for <i>x<\/i>.\r\n<h4>Answer<\/h4>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185336\/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\"]First, 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\n\r\n<h4>Answer<\/h4>\r\nmake graph for this example[\/hidden-answer]\r\n<h4><\/h4>\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Graph an Equation Using Intercepts\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>&#8211; and <em>y<\/em>-intercepts<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<h2 id=\"Intercepts\">Intercepts<\/h2>\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<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 <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\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185331\/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 (0, 2).<\/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>&#8211; and <em>y<\/em>-intercepts of a linear equation, you can substitute 0 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<h2><span style=\"color: #4588bf\">Using Intercepts to Graph Lines<\/span><\/h2>\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>Let\u2019s do it 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\u2019s 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\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185333\/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\">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 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>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\\\\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>To find the <i>x<\/i>-intercept, set [latex]y=0[\/latex] and solve for <i>x<\/i>.<\/p>\n<h4>Answer<\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185336\/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\">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<h4>Answer<\/h4>\n<p>make graph for this example<\/p><\/div>\n<\/div>\n<h4><\/h4>\n<\/div>\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-4623\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Graph Linear Equations Using Intercepts. <strong>Authored by<\/strong>: mathispower4u. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/k8r-q_T6UFk\">https:\/\/youtu.be\/k8r-q_T6UFk<\/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":17533,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Graph Linear Equations Using Intercepts\",\"author\":\"mathispower4u\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/k8r-q_T6UFk\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"e15e8d51-7121-47cc-979f-07c7ad4756db","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4623","chapter","type-chapter","status-publish","hentry"],"part":4587,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters\/4623","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters\/4623\/revisions"}],"predecessor-version":[{"id":5076,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters\/4623\/revisions\/5076"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/parts\/4587"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters\/4623\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/media?parent=4623"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapter-type?post=4623"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/contributor?post=4623"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/license?post=4623"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}