{"id":1115,"date":"2015-11-12T18:35:32","date_gmt":"2015-11-12T18:35:32","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=1115"},"modified":"2015-11-12T18:35:32","modified_gmt":"2015-11-12T18:35:32","slug":"key-concepts-glossary-48","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/key-concepts-glossary-48\/","title":{"raw":"Key Concepts &amp; Glossary","rendered":"Key Concepts &amp; Glossary"},"content":{"raw":"<h2 data-type=\"title\">Key Concepts<\/h2>\n<ul id=\"fs-id1165134190780\"><li>Linear functions may be graphed by plotting points or by using the <em data-effect=\"italics\">y<\/em>-intercept and slope.<\/li>\n\t<li>Graphs of linear functions may be transformed by using shifts up, down, left, or right, as well as through stretches, compressions, and reflections.<\/li>\n\t<li>The <em data-effect=\"italics\">y<\/em>-intercept and slope of a line may be used to write the equation of a line.<\/li>\n\t<li>The <em data-effect=\"italics\">x<\/em>-intercept is the point at which the graph of a linear function crosses the <em data-effect=\"italics\">x<\/em>-axis.<\/li>\n\t<li>Horizontal lines are written in the form, <em>f<\/em>(<em>x<\/em>) = <em>b<\/em>.<\/li>\n\t<li>Vertical lines are written in the form, <em>x\u00a0<\/em>= <em>b<\/em>.<\/li>\n\t<li>Parallel lines have the same slope.<\/li>\n\t<li>Perpendicular lines have negative reciprocal slopes, assuming neither is vertical.<\/li>\n\t<li>A line parallel to another line, passing through a given point, may be found by substituting the slope value of the line and the <em data-effect=\"italics\">x<\/em>- and <em data-effect=\"italics\">y<\/em>-values of the given point into the equation, [latex]f\\left(x\\right)=mx+b\\\\[\/latex], and using the <em>b<\/em>\u00a0that results. Similarly, the point-slope form of an equation can also be used.<\/li>\n\t<li>A line perpendicular to another line, passing through a given point, may be found in the same manner, with the exception of using the negative reciprocal slope.<\/li>\n\t<li>A system of linear equations may be solved setting the two equations equal to one another and solving for <em>x<\/em>. The <em data-effect=\"italics\">y<\/em>-value may be found by evaluating either one of the original equations using this <em data-effect=\"italics\">x<\/em>-value.<\/li>\n\t<li>A system of linear equations may also be solved by finding the point of intersection on a graph.<\/li>\n<\/ul><div data-type=\"glossary\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id1165137572723\" class=\"definition\"><dt><strong>horizontal line<\/strong><\/dt><dd id=\"fs-id1165137572728\">a line defined by [latex]f\\left(x\\right)=b\\\\[\/latex], where <em>b<\/em>\u00a0is a real number. The slope of a horizontal line is 0.<\/dd><\/dl><dl id=\"fs-id1165135330621\" class=\"definition\"><dt><strong>parallel lines<\/strong><\/dt><dd id=\"fs-id1165135186582\">two or more lines with the same slope<\/dd><\/dl><dl id=\"fs-id1165135186586\" class=\"definition\"><dt><strong>perpendicular lines<\/strong><\/dt><dd id=\"fs-id1165135186592\">two lines that intersect at right angles and have slopes that are negative reciprocals of each other<\/dd><\/dl><dl id=\"fs-id1165135186597\" class=\"definition\"><dt><strong>vertical line<\/strong><\/dt><dd id=\"fs-id1165137757647\">a line defined by <em>x<\/em> = <em>a<\/em>, where <em>a<\/em>\u00a0is a real number. The slope of a vertical line is undefined.<\/dd><\/dl><dl id=\"fs-id1165137757668\" class=\"definition\"><dt><strong><em>x<\/em>-intercept<\/strong><\/dt><dd id=\"fs-id1165137782278\">the point on the graph of a linear function when the output value is 0; the point at which the graph crosses the horizontal axis<\/dd><\/dl><\/div>\n\u00a0","rendered":"<h2 data-type=\"title\">Key Concepts<\/h2>\n<ul id=\"fs-id1165134190780\">\n<li>Linear functions may be graphed by plotting points or by using the <em data-effect=\"italics\">y<\/em>-intercept and slope.<\/li>\n<li>Graphs of linear functions may be transformed by using shifts up, down, left, or right, as well as through stretches, compressions, and reflections.<\/li>\n<li>The <em data-effect=\"italics\">y<\/em>-intercept and slope of a line may be used to write the equation of a line.<\/li>\n<li>The <em data-effect=\"italics\">x<\/em>-intercept is the point at which the graph of a linear function crosses the <em data-effect=\"italics\">x<\/em>-axis.<\/li>\n<li>Horizontal lines are written in the form, <em>f<\/em>(<em>x<\/em>) = <em>b<\/em>.<\/li>\n<li>Vertical lines are written in the form, <em>x\u00a0<\/em>= <em>b<\/em>.<\/li>\n<li>Parallel lines have the same slope.<\/li>\n<li>Perpendicular lines have negative reciprocal slopes, assuming neither is vertical.<\/li>\n<li>A line parallel to another line, passing through a given point, may be found by substituting the slope value of the line and the <em data-effect=\"italics\">x<\/em>&#8211; and <em data-effect=\"italics\">y<\/em>-values of the given point into the equation, [latex]f\\left(x\\right)=mx+b\\\\[\/latex], and using the <em>b<\/em>\u00a0that results. Similarly, the point-slope form of an equation can also be used.<\/li>\n<li>A line perpendicular to another line, passing through a given point, may be found in the same manner, with the exception of using the negative reciprocal slope.<\/li>\n<li>A system of linear equations may be solved setting the two equations equal to one another and solving for <em>x<\/em>. The <em data-effect=\"italics\">y<\/em>-value may be found by evaluating either one of the original equations using this <em data-effect=\"italics\">x<\/em>-value.<\/li>\n<li>A system of linear equations may also be solved by finding the point of intersection on a graph.<\/li>\n<\/ul>\n<div data-type=\"glossary\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id1165137572723\" class=\"definition\">\n<dt><strong>horizontal line<\/strong><\/dt>\n<dd id=\"fs-id1165137572728\">a line defined by [latex]f\\left(x\\right)=b\\\\[\/latex], where <em>b<\/em>\u00a0is a real number. The slope of a horizontal line is 0.<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135330621\" class=\"definition\">\n<dt><strong>parallel lines<\/strong><\/dt>\n<dd id=\"fs-id1165135186582\">two or more lines with the same slope<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135186586\" class=\"definition\">\n<dt><strong>perpendicular lines<\/strong><\/dt>\n<dd id=\"fs-id1165135186592\">two lines that intersect at right angles and have slopes that are negative reciprocals of each other<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135186597\" class=\"definition\">\n<dt><strong>vertical line<\/strong><\/dt>\n<dd id=\"fs-id1165137757647\">a line defined by <em>x<\/em> = <em>a<\/em>, where <em>a<\/em>\u00a0is a real number. The slope of a vertical line is undefined.<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137757668\" class=\"definition\">\n<dt><strong><em>x<\/em>-intercept<\/strong><\/dt>\n<dd id=\"fs-id1165137782278\">the point on the graph of a linear function when the output value is 0; the point at which the graph crosses the horizontal axis<\/dd>\n<\/dl>\n<\/div>\n<p>\u00a0<\/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-1115\">\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>Precalculus. <strong>Authored by<\/strong>: Jay Abramson, et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.<\/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":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Precalculus\",\"author\":\"Jay Abramson, et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1115","chapter","type-chapter","status-publish","hentry"],"part":1083,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1115","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1115\/revisions"}],"predecessor-version":[{"id":2450,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1115\/revisions\/2450"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/1083"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1115\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/media?parent=1115"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1115"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/contributor?post=1115"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/license?post=1115"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}