{"id":51,"date":"2017-08-23T07:12:48","date_gmt":"2017-08-23T07:12:48","guid":{"rendered":"http:\/\/americanboard.org\/Subjects\/mathematics\/?page_id=51"},"modified":"2017-09-18T15:11:42","modified_gmt":"2017-09-18T15:11:42","slug":"finding-the-equation-of-a-line","status":"publish","type":"page","link":"https:\/\/americanboard.org\/Subjects\/mathematics\/finding-the-equation-of-a-line\/","title":{"rendered":"Finding the Equation of a Line"},"content":{"rendered":"<div class=\"twelve columns\" style=\"margin-top: 10%;\">\n<div class=\"advance\"><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/graphing-linear-equations-and-inequalities\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/algebra-functions-i\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/algebra-functions-ii\">Next Workshop \u27a1<\/a><\/div>\n<p><!-- CONTENT BEGINS HERE --><\/p>\n<h1 id=\"title\">Finding the Equation of a Line<\/h1>\n<h4>Objective<\/h4>\n<p>In this lesson, we will study how to find the equation of a line.<\/p>\n<h4>Previously Covered:<\/h4>\n<ul>\n<li>The <em><strong>standard form\u00a0<\/strong><\/em>of a <strong><em>linear equation<\/em><\/strong> is <em>ax\u00a0+ by = c. <\/em><\/li>\n<li>The <strong><em>slope-intercept\u00a0<\/em><\/strong>form of an equation is <em>y\u00a0= mx + b.<\/em><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images2\/s6_p1_clip_image002.gif\" width=\"174\" height=\"38\" name=\"graphics2\" align=\"ABSMIDDLE\" border=\"0\" \/><\/li>\n<\/ul>\n<section>\n<h3><strong>How do we locate a line on the coordinate plane?<\/strong><\/h3>\n<p>The slope of a line indicates how steep it is. To locate a line\u00a0on a coordinate plane, however, we must know at least one point on\u00a0the line as well as the line&#8217;s slope.<\/p>\n<p>Remember that the <em>y<\/em>-intercept is the value of <em>y<\/em> where the line crosses the <em>y<\/em>-axis. In other words, it is the value of <em>y\u00a0<\/em>where <em>x = 0.<\/em> In the slope-intercept form of an equation, <em>b<\/em> is the<em> y-<\/em>intercept. Therefore, if we know the slope and the <em>y<\/em>-intercept, we are able to find equation of the line in slope-intercept form.<\/p>\n<h3><strong>What if we know the slope and a point other than the\u00a0<em>y<\/em>-intercept?<\/strong><\/h3>\n<p>For example, we know a line contains the point (2, 3) and has a\u00a0slope of 2. By plugging the slope into slope-intercept form we\u00a0find that <em>y = 2x + b.<\/em><\/p>\n<p>Graph the point (2, 3).\u00a0From there, move 2 units up and 1 unit right to find a\u00a0second point.<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images2\/Math%20Mod%202%5B1%5D.2%20art%20011.JPG\" width=\"350\" height=\"318\" name=\"graphics3\" align=\"BOTTOM\" border=\"0\" \/><\/p>\n<p>In effect, we have substituted the values from the point we\u00a0know into the slope formula.<\/p>\n<p align=\"CENTER\"><em><img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images2\/s6_p2_clip_image002.gif\" width=\"98\" height=\"76\" name=\"graphics4\" align=\"BOTTOM\" border=\"0\" \/><\/em><\/p>\n<p>Then multiply both sides of the equation by (<em>x\u00a0\u2013 2)<\/em> and\u00a0simplify to solve for <em>y.<\/em><\/p>\n<p align=\"CENTER\"><em><img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images2\/s6_p2_clip_image004.gif\" width=\"152\" height=\"132\" name=\"graphics5\" align=\"BOTTOM\" border=\"0\" \/><\/em><\/p>\n<p>We now have the slope-intercept form of the equation, which was\u00a0simplified from point-slope form of the equation in step two\u00a0above. To generalize point-slope form, the equation of a line\u00a0through a point (<em>x<sub>1<\/sub>, y<sub>1<\/sub><\/em>) is\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images2\/s6_p2_clip_image006.gif\" width=\"110\" height=\"15\" name=\"graphics6\" align=\"ABSMIDDLE\" border=\"0\" \/>,where\u00a0<em>m\u00a0<\/em>is the slope.<\/p>\n<h3><strong>What if we know the <em>x<\/em>&#8211; and <em>y<\/em>-intercepts,\u00a0but not the slope?<\/strong><\/h3>\n<p>If you know the <em>x<\/em>&#8211;\u00a0and <em>y<\/em>-intercepts,\u00a0substitute the values of those points into the formula for\u00a0slope.<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images2\/s6_p3_clip_image002.gif\" width=\"72\" height=\"34\" name=\"graphics3\" align=\"BOTTOM\" border=\"0\" \/><\/p>\n<p>Then substitute the slope into slope-intercept form.<\/p>\n<p>For example, given the points (12, 0) and (9, 1), find the\u00a0equation of the line in point-slope form.<\/p>\n<p>First, use the two points given to find the slope.<\/p>\n<p align=\"CENTER\"><em><img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images2\/s6_p3_clip_image008.gif\" width=\"94\" height=\"123\" name=\"graphics4\" align=\"BOTTOM\" border=\"0\" \/><\/em><\/p>\n<p>Then substitute the values of one point and the slope into the\u00a0equation\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images2\/s6_p3_clip_image010.gif\" width=\"110\" height=\"15\" name=\"graphics5\" align=\"ABSMIDDLE\" border=\"0\" \/>.<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images2\/s6_p3_clip_image012.gif\" width=\"130\" height=\"145\" name=\"graphics6\" align=\"BOTTOM\" border=\"0\" \/><\/p>\n<p>The slope is\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images2\/s6_p3_clip_image014.gif\" width=\"20\" height=\"34\" name=\"graphics7\" align=\"ABSMIDDLE\" border=\"0\" \/>\u00a0and the <em>y<\/em>-intercept\u00a0is (0, 4).<\/p>\n<h3>Review of New Concepts and Terms<\/h3>\n<ul>\n<li>An <em><strong>equation<\/strong><\/em> is a statement that shows that two mathematical expressions are equal.<\/li>\n<li>In a <em><strong>linear equation<\/strong><\/em>, no variable has an exponent greater than one.<\/li>\n<li>An equation in the form <em>ax\u00a0+ b = 0<\/em> is a <strong><em>linear equation in one\u00a0variable<\/em><\/strong>. It is also called a <strong><em>first-degree\u00a0equation in one variable<\/em><\/strong>.\u00a0In <strong><em>standard\u00a0form<\/em><\/strong>,\u00a0a linear equation in two variables is in the form <em>ax\u00a0+ by = c, <\/em>where\u00a0<em>a, b, <\/em>and\u00a0<em>c\u00a0<\/em>are constants, and not all are equal to zero.<\/li>\n<li>In a <strong><em>linear\u00a0inequality<\/em><\/strong>, the symbol <em><img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images\/s2_p4_clip_image008.gif\" width=\"7\" height=\"8\" name=\"graphics3\" align=\"BOTTOM\" border=\"0\" \/>\u00a0<\/em>means <em>greater than<\/em>,\u00a0<em><img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images\/s2_p4_clip_image002.gif\" width=\"7\" height=\"8\" name=\"graphics4\" align=\"BOTTOM\" border=\"0\" \/>\u00a0<\/em>means <em>less than<\/em>,\u00a0<em><img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images\/s2_p4_clip_image005.gif\" width=\"9\" height=\"10\" name=\"graphics5\" align=\"BOTTOM\" border=\"0\" \/>\u00a0<\/em>means <em>less than or equal\u00a0to<\/em>, and\u00a0<em><img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images\/s2_p4_clip_image011.gif\" width=\"9\" height=\"10\" name=\"graphics6\" align=\"BOTTOM\" border=\"0\" \/>\u00a0<\/em>means <em>greater than\u00a0or equal to<\/em>.<\/li>\n<li>The <em><strong>standard form\u00a0<\/strong><\/em>of a <em><strong>linear equation<\/strong><\/em> is <em>ax\u00a0+ by = c. <\/em><\/li>\n<li>The <em><strong>slope-intercept\u00a0<\/strong><\/em>form of an equation is <em>y\u00a0= mx + b.<\/em><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"no_margin non_block_image\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/2\/images2\/s7_p1_clip_image002.gif\" width=\"174\" height=\"38\" name=\"graphics7\" align=\"ABSMIDDLE\" border=\"0\" \/><\/li>\n<\/ul>\n<h3>Further Reading<\/h3>\n<p><em>Algebra<\/em> <em>Demystified: A Self-teaching Guide <\/em>(Rhonda Huettenmueller): McGraw-Hill,\u00a02003.<\/p>\n<p><em>College Algebra<\/em> (Ron Larson and Robert P. Hostetler): Houghton Mifflin, 2003.<\/p>\n<p><em>Practical Algebra: A Self-Teaching Guide<\/em> (Peter H. Selby and Steve Slavin): John Wiley and\u00a0Sons, 1991.<\/p>\n<p><em>Schaum&#8217;s Outline of Intermediate Algebra<\/em> (Ray Steege and Kerry Bailey): McGraw Hill,\u00a01997.<\/p>\n<p align=\"center\"><strong><em>Don&#8217;t forget to test your knowledge with the <a href=\" http:\/\/www.abcte.org\/drupal\/courses\/mrc\/quizzes\/algfunct1\" target=\"popsome\"> Algebra and Functions I\u00a0Chapter Quiz; <\/a><\/em><\/strong><\/p>\n<\/section>\n<div class=\"advance\"><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/graphing-linear-equations-and-inequalities\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/algebra-functions-i\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/algebra-functions-ii\">Next Workshop \u27a1<\/a><\/div>\n<p><a class=\"backtotop\" href=\"#title\">Back to Top<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u2b05 Previous Lesson\u00a0Workshop Index\u00a0Next Workshop \u27a1 Finding the Equation of a Line Objective In this lesson, we will study how to find the equation of a line. Previously Covered: The standard form\u00a0of a linear equation is ax\u00a0+ by = c. The slope-intercept\u00a0form of an equation is y\u00a0= mx + b. How do we locate a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-51","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/51","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/comments?post=51"}],"version-history":[{"count":12,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/51\/revisions"}],"predecessor-version":[{"id":732,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/51\/revisions\/732"}],"wp:attachment":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/media?parent=51"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}