{"id":937,"date":"2016-10-20T20:49:09","date_gmt":"2016-10-20T20:49:09","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/?post_type=chapter&#038;p=937"},"modified":"2017-08-15T20:56:37","modified_gmt":"2017-08-15T20:56:37","slug":"introduction-writing-equations-of-lines","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/chapter\/introduction-writing-equations-of-lines\/","title":{"raw":"Introduction to Equations of Lines","rendered":"Introduction to Equations of Lines"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nEquations of Lines\r\n<ul>\r\n \t<li>Write equations of lines in slope-intercept, point-slope, and standard forms<\/li>\r\n \t<li>Identify the equations and graphs of horizontal and vertical lines<\/li>\r\n \t<li>Determine whether two lines are parallel, perpendicular, or neither<\/li>\r\n \t<li>Write equations of lines that are parallel or perpendicular to another line<\/li>\r\n<\/ul>\r\n<\/div>\r\nNow that we've learned how to plot points on a coordinate plane and graph linear equations, we can begin to analyze the equations of lines and evaluate\u00a0the different characteristics\u00a0of these lines. In this section, we'll learn about the commonly used forms for writing linear equations and the properties\u00a0of lines that can be determined from their equations.\r\n\r\nFor example, without creating a table of values, you will be able to match each equation below to its corresponding graph. You will also be able to explain the similarities and differences of each line, how they relate to each other, and why they behave that way.\r\n\r\n&nbsp;\r\n\r\n<img class=\" wp-image-4156 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/04\/13224212\/Screen-Shot-2017-04-13-at-3.42.26-PM-300x270.png\" alt=\"6 lines graphed on a coordinate plane.\" width=\"441\" height=\"397\" \/>\r\n\r\n(a) [latex]y=3x+2[\/latex]\r\n\r\n(b) [latex]y-4=-\\frac{1}{2}(x+2)[\/latex]\r\n\r\n(c) [latex]x=5[\/latex]\r\n\r\n(d) [latex]y=-2[\/latex]\r\n\r\n(e) [latex]3x=y+1[\/latex]\r\n\r\n(f) [latex]2y-3x=6[\/latex]\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>Equations of Lines<\/p>\n<ul>\n<li>Write equations of lines in slope-intercept, point-slope, and standard forms<\/li>\n<li>Identify the equations and graphs of horizontal and vertical lines<\/li>\n<li>Determine whether two lines are parallel, perpendicular, or neither<\/li>\n<li>Write equations of lines that are parallel or perpendicular to another line<\/li>\n<\/ul>\n<\/div>\n<p>Now that we&#8217;ve learned how to plot points on a coordinate plane and graph linear equations, we can begin to analyze the equations of lines and evaluate\u00a0the different characteristics\u00a0of these lines. In this section, we&#8217;ll learn about the commonly used forms for writing linear equations and the properties\u00a0of lines that can be determined from their equations.<\/p>\n<p>For example, without creating a table of values, you will be able to match each equation below to its corresponding graph. You will also be able to explain the similarities and differences of each line, how they relate to each other, and why they behave that way.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4156 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/04\/13224212\/Screen-Shot-2017-04-13-at-3.42.26-PM-300x270.png\" alt=\"6 lines graphed on a coordinate plane.\" width=\"441\" height=\"397\" \/><\/p>\n<p>(a) [latex]y=3x+2[\/latex]<\/p>\n<p>(b) [latex]y-4=-\\frac{1}{2}(x+2)[\/latex]<\/p>\n<p>(c) [latex]x=5[\/latex]<\/p>\n<p>(d) [latex]y=-2[\/latex]<\/p>\n<p>(e) [latex]3x=y+1[\/latex]<\/p>\n<p>(f) [latex]2y-3x=6[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/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-937\">\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>Introduction and Learning Objectives. <strong>Provided 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>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Introduction and Learning Objectives\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"b7a4605c-14de-428c-8df0-65168f2efe9e","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-937","chapter","type-chapter","status-publish","hentry"],"part":17,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/937","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":15,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/937\/revisions"}],"predecessor-version":[{"id":4403,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/937\/revisions\/4403"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/17"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/937\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/media?parent=937"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=937"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/contributor?post=937"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/license?post=937"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}