{"id":10700,"date":"2017-06-05T15:05:27","date_gmt":"2017-06-05T15:05:27","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10700"},"modified":"2024-04-30T23:17:08","modified_gmt":"2024-04-30T23:17:08","slug":"summary-identifying-and-using-slope","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/summary-identifying-and-using-slope\/","title":{"raw":"Summary: Finding Slope","rendered":"Summary: Finding Slope"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<strong>Find the slope from a graph<\/strong>\r\n<ol id=\"eip-id1170322684949\" class=\"stepwise\">\r\n \t<li>Locate two points on the line whose coordinates are integers.<\/li>\r\n \t<li>Starting with the point on the left, sketch a right triangle, going from the first point to the second point.<\/li>\r\n \t<li>Count the rise and the run on the legs of the triangle.<\/li>\r\n \t<li>Take the ratio of rise to run to find the slope, [latex]m={\\Large\\frac{\\text{rise}}{\\text{run}}}[\/latex]<\/li>\r\n<\/ol>\r\n<ul id=\"eip-678\">\r\n \t<li><strong>Slope of a Horizontal Line<\/strong>\r\n<ul id=\"eip-id1170320559493\">\r\n \t<li>The slope of a horizontal line, [latex]y=b[\/latex] , is [latex]0[\/latex].<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Slope of a Vertical Line<\/strong>\r\n<ul id=\"eip-id1170323909195\">\r\n \t<li>The slope of a vertical line, [latex]x=a[\/latex] , is undefined.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Slope Formula<\/strong>\r\n<ul id=\"eip-id1170322772650\">\r\n \t<li>The slope of the line between two points [latex]\\left({x}_{1},{y}_{1}\\right)[\/latex] and [latex]\\left({x}_{2},{y}_{2}\\right)[\/latex] is [latex]m={\\Large\\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Graph a line given a point and a slope.<\/strong>\r\n<ol id=\"eip-id1170326457932\" class=\"stepwise\">\r\n \t<li>Plot the given point.<\/li>\r\n \t<li>Use the slope formula to identify the rise and the run.<\/li>\r\n \t<li>Starting at the given point, count out the rise and run to mark the second point.<\/li>\r\n \t<li>Connect the points with a line.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n&nbsp;\r\n<h2>Glossary<\/h2>\r\n<dl id=\"fs-id1726430\" class=\"definition\">\r\n \t<dt>slope of a line<\/dt>\r\n \t<dd id=\"fs-id1726435\">The slope of a line is [latex]m={\\Large\\frac{\\text{rise}}{\\text{run}}}[\/latex] . The rise measures the vertical change and the run measures the horizontal change.<\/dd>\r\n<\/dl>","rendered":"<h2>Key Concepts<\/h2>\n<p><strong>Find the slope from a graph<\/strong><\/p>\n<ol id=\"eip-id1170322684949\" class=\"stepwise\">\n<li>Locate two points on the line whose coordinates are integers.<\/li>\n<li>Starting with the point on the left, sketch a right triangle, going from the first point to the second point.<\/li>\n<li>Count the rise and the run on the legs of the triangle.<\/li>\n<li>Take the ratio of rise to run to find the slope, [latex]m={\\Large\\frac{\\text{rise}}{\\text{run}}}[\/latex]<\/li>\n<\/ol>\n<ul id=\"eip-678\">\n<li><strong>Slope of a Horizontal Line<\/strong>\n<ul id=\"eip-id1170320559493\">\n<li>The slope of a horizontal line, [latex]y=b[\/latex] , is [latex]0[\/latex].<\/li>\n<\/ul>\n<\/li>\n<li><strong>Slope of a Vertical Line<\/strong>\n<ul id=\"eip-id1170323909195\">\n<li>The slope of a vertical line, [latex]x=a[\/latex] , is undefined.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Slope Formula<\/strong>\n<ul id=\"eip-id1170322772650\">\n<li>The slope of the line between two points [latex]\\left({x}_{1},{y}_{1}\\right)[\/latex] and [latex]\\left({x}_{2},{y}_{2}\\right)[\/latex] is [latex]m={\\Large\\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li><strong>Graph a line given a point and a slope.<\/strong>\n<ol id=\"eip-id1170326457932\" class=\"stepwise\">\n<li>Plot the given point.<\/li>\n<li>Use the slope formula to identify the rise and the run.<\/li>\n<li>Starting at the given point, count out the rise and run to mark the second point.<\/li>\n<li>Connect the points with a line.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1726430\" class=\"definition\">\n<dt>slope of a line<\/dt>\n<dd id=\"fs-id1726435\">The slope of a line is [latex]m={\\Large\\frac{\\text{rise}}{\\text{run}}}[\/latex] . The rise measures the vertical change and the run measures the horizontal change.<\/dd>\n<\/dl>\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-10700\">\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>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <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\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/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":11,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","CANDELA_OUTCOMES_GUID":"012082040f0848959b64162572e7cb1a","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-10700","chapter","type-chapter","status-publish","hentry"],"part":8524,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10700","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10700\/revisions"}],"predecessor-version":[{"id":18059,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10700\/revisions\/18059"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/8524"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10700\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/media?parent=10700"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=10700"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=10700"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/license?post=10700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}