{"id":367,"date":"2015-10-26T17:30:01","date_gmt":"2015-10-26T17:30:01","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=367"},"modified":"2015-11-12T18:38:00","modified_gmt":"2015-11-12T18:38:00","slug":"key-concepts-glossary-8","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/chapter\/key-concepts-glossary-8\/","title":{"raw":"Key Concepts &amp; Glossary","rendered":"Key Concepts &amp; Glossary"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n\t<li>We can solve linear equations in one variable in the form [latex]ax+b=0[\/latex] using standard algebraic properties.<\/li>\r\n\t<li>A rational expression is a quotient of two polynomials. We use the LCD to clear the fractions from an equation.<\/li>\r\n\t<li>All solutions to a rational equation should be verified within the original equation to avoid an undefined term, or zero in the denominator.<\/li>\r\n\t<li>Given two points, we can find the slope of a line using the slope formula.<\/li>\r\n\t<li>We can identify the slope and <em>y<\/em>-intercept of an equation in slope-intercept form.<\/li>\r\n\t<li>We can find the equation of a line given the slope and a point.<\/li>\r\n\t<li>We can also find the equation of a line given two points. Find the slope and use the point-slope formula.<\/li>\r\n\t<li>The standard form of a line has no fractions.<\/li>\r\n\t<li>Horizontal lines have a slope of zero and are defined as [latex]y=c[\/latex], where <em>c <\/em>is a constant.<\/li>\r\n\t<li>Vertical lines have an undefined slope (zero in the denominator), and are defined as [latex]x=c[\/latex], where <em>c <\/em>is a constant.<\/li>\r\n\t<li>Parallel lines have the same slope and different <em>y-<\/em>intercepts.<\/li>\r\n\t<li>Perpendicular lines have slopes that are negative reciprocals of each other unless one is horizontal and the other is vertical.<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<strong>conditional equation<\/strong> an equation that is true for some values of the variable\r\n\r\n<strong>identity equation<\/strong> an equation that is true for all values of the variable\r\n\r\n<strong>inconsistent equation<\/strong> an equation producing a false result\r\n\r\n<strong>linear equation<\/strong> an algebraic equation in which each term is either a constant or the product of a constant and the first power of a variable\r\n\r\n<strong>solution set<\/strong> the set of all solutions to an equation\r\n\r\n<strong>slope<\/strong> the change in <em>y-<\/em>values over the change in <em>x-<\/em>values\r\n\r\n<strong>rational equation<\/strong> an equation consisting of a fraction of polynomials","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li>We can solve linear equations in one variable in the form [latex]ax+b=0[\/latex] using standard algebraic properties.<\/li>\n<li>A rational expression is a quotient of two polynomials. We use the LCD to clear the fractions from an equation.<\/li>\n<li>All solutions to a rational equation should be verified within the original equation to avoid an undefined term, or zero in the denominator.<\/li>\n<li>Given two points, we can find the slope of a line using the slope formula.<\/li>\n<li>We can identify the slope and <em>y<\/em>-intercept of an equation in slope-intercept form.<\/li>\n<li>We can find the equation of a line given the slope and a point.<\/li>\n<li>We can also find the equation of a line given two points. Find the slope and use the point-slope formula.<\/li>\n<li>The standard form of a line has no fractions.<\/li>\n<li>Horizontal lines have a slope of zero and are defined as [latex]y=c[\/latex], where <em>c <\/em>is a constant.<\/li>\n<li>Vertical lines have an undefined slope (zero in the denominator), and are defined as [latex]x=c[\/latex], where <em>c <\/em>is a constant.<\/li>\n<li>Parallel lines have the same slope and different <em>y-<\/em>intercepts.<\/li>\n<li>Perpendicular lines have slopes that are negative reciprocals of each other unless one is horizontal and the other is vertical.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>conditional equation<\/strong> an equation that is true for some values of the variable<\/p>\n<p><strong>identity equation<\/strong> an equation that is true for all values of the variable<\/p>\n<p><strong>inconsistent equation<\/strong> an equation producing a false result<\/p>\n<p><strong>linear equation<\/strong> an algebraic equation in which each term is either a constant or the product of a constant and the first power of a variable<\/p>\n<p><strong>solution set<\/strong> the set of all solutions to an equation<\/p>\n<p><strong>slope<\/strong> the change in <em>y-<\/em>values over the change in <em>x-<\/em>values<\/p>\n<p><strong>rational equation<\/strong> an equation consisting of a fraction of polynomials<\/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-367\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: OpenStax College Algebra. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface<\/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":276,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"College Algebra\",\"author\":\"OpenStax College Algebra\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\",\"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-367","chapter","type-chapter","status-publish","hentry"],"part":208,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/367","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/367\/revisions"}],"predecessor-version":[{"id":649,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/367\/revisions\/649"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/208"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/367\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/media?parent=367"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=367"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/contributor?post=367"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/license?post=367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}