{"id":1494,"date":"2015-11-12T18:35:28","date_gmt":"2015-11-12T18:35:28","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=1494"},"modified":"2017-04-03T14:51:48","modified_gmt":"2017-04-03T14:51:48","slug":"key-concepts-glossary-38","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/key-concepts-glossary-38\/","title":{"raw":"Key Concepts &amp; Glossary","rendered":"Key Concepts &amp; Glossary"},"content":{"raw":"<section id=\"fs-id1165137898092\" class=\"key-equations\" data-depth=\"1\"><h1 data-type=\"title\">Key Equations<\/h1>\r\n<table id=\"eip-id1165133094986\" summary=\"..\"><tbody><tr><td data-valign=\"middle\" data-align=\"left\">Direct variation<\/td>\r\n<td>[latex]y=k{x}^{n},k\\text{ is a nonzero constant}[\/latex].<\/td>\r\n<\/tr><tr><td data-valign=\"middle\" data-align=\"left\">Inverse variation<\/td>\r\n<td>[latex]y=\\frac{k}{{x}^{n}},k\\text{ is a nonzero constant}[\/latex].<\/td>\r\n<\/tr><\/tbody><\/table><\/section><section id=\"fs-id1165137419773\" class=\"key-concepts\" data-depth=\"1\"><h1 data-type=\"title\">Key Concepts<\/h1>\r\n<ul id=\"fs-id1165137723142\"><li>A relationship where one quantity is a constant multiplied by another quantity is called direct variation.<\/li>\r\n\t<li>Two variables that are directly proportional to one another will have a constant ratio.<\/li>\r\n\t<li>A relationship where one quantity is a constant divided by another quantity is called inverse variation.<\/li>\r\n\t<li>Two variables that are inversely proportional to one another will have a constant multiple.<\/li>\r\n\t<li>In many problems, a variable varies directly or inversely with multiple variables. We call this type of relationship joint variation.<\/li>\r\n<\/ul><h2 data-type=\"glossary-title\">Glossary<\/h2>\r\n<dl id=\"fs-id1165137735724\" class=\"definition\"><dt><strong>constant of variation<\/strong><\/dt><dd id=\"fs-id1165137735729\">the non-zero value <em>k<\/em>\u00a0that helps define the relationship between variables in direct or inverse variation<\/dd><\/dl><dl id=\"fs-id1165137762202\" class=\"definition\"><dt><strong>direct variation<\/strong><\/dt><dd id=\"fs-id1165137762208\">the relationship between two variables that are a constant multiple of each other; as one quantity increases, so does the other<\/dd><\/dl><dl id=\"fs-id1165137462046\" class=\"definition\"><dt><strong>inverse variation<\/strong><\/dt><dd id=\"fs-id1165137462052\">the relationship between two variables in which the product of the variables is a constant<\/dd><\/dl><dl id=\"fs-id1165135501040\" class=\"definition\"><dt><strong>inversely proportional<\/strong><\/dt><dd id=\"fs-id1165137874542\">a relationship where one quantity is a constant divided by the other quantity; as one quantity increases, the other decreases<\/dd><\/dl><dl id=\"fs-id1165137874546\" class=\"definition\"><dt><strong>joint variation<\/strong><\/dt><dd id=\"fs-id1165135696715\">a relationship where a variable varies directly or inversely with multiple variables<\/dd><\/dl><dl id=\"fs-id1165135696718\" class=\"definition\"><dt><strong>varies directly<\/strong><\/dt><dd id=\"fs-id1165137432955\">a relationship where one quantity is a constant multiplied by the other quantity<\/dd><\/dl><dl id=\"fs-id1165137432958\" class=\"definition\"><dt><strong>varies inversely<\/strong><\/dt><dd id=\"fs-id1165135439853\">a relationship where one quantity is a constant divided by the other quantity<\/dd><\/dl><\/section>","rendered":"<section id=\"fs-id1165137898092\" class=\"key-equations\" data-depth=\"1\">\n<h1 data-type=\"title\">Key Equations<\/h1>\n<table id=\"eip-id1165133094986\" summary=\"..\">\n<tbody>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Direct variation<\/td>\n<td>[latex]y=k{x}^{n},k\\text{ is a nonzero constant}[\/latex].<\/td>\n<\/tr>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Inverse variation<\/td>\n<td>[latex]y=\\frac{k}{{x}^{n}},k\\text{ is a nonzero constant}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<section id=\"fs-id1165137419773\" class=\"key-concepts\" data-depth=\"1\">\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"fs-id1165137723142\">\n<li>A relationship where one quantity is a constant multiplied by another quantity is called direct variation.<\/li>\n<li>Two variables that are directly proportional to one another will have a constant ratio.<\/li>\n<li>A relationship where one quantity is a constant divided by another quantity is called inverse variation.<\/li>\n<li>Two variables that are inversely proportional to one another will have a constant multiple.<\/li>\n<li>In many problems, a variable varies directly or inversely with multiple variables. We call this type of relationship joint variation.<\/li>\n<\/ul>\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id1165137735724\" class=\"definition\">\n<dt><strong>constant of variation<\/strong><\/dt>\n<dd id=\"fs-id1165137735729\">the non-zero value <em>k<\/em>\u00a0that helps define the relationship between variables in direct or inverse variation<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137762202\" class=\"definition\">\n<dt><strong>direct variation<\/strong><\/dt>\n<dd id=\"fs-id1165137762208\">the relationship between two variables that are a constant multiple of each other; as one quantity increases, so does the other<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137462046\" class=\"definition\">\n<dt><strong>inverse variation<\/strong><\/dt>\n<dd id=\"fs-id1165137462052\">the relationship between two variables in which the product of the variables is a constant<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135501040\" class=\"definition\">\n<dt><strong>inversely proportional<\/strong><\/dt>\n<dd id=\"fs-id1165137874542\">a relationship where one quantity is a constant divided by the other quantity; as one quantity increases, the other decreases<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137874546\" class=\"definition\">\n<dt><strong>joint variation<\/strong><\/dt>\n<dd id=\"fs-id1165135696715\">a relationship where a variable varies directly or inversely with multiple variables<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135696718\" class=\"definition\">\n<dt><strong>varies directly<\/strong><\/dt>\n<dd id=\"fs-id1165137432955\">a relationship where one quantity is a constant multiplied by the other quantity<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137432958\" class=\"definition\">\n<dt><strong>varies inversely<\/strong><\/dt>\n<dd id=\"fs-id1165135439853\">a relationship where one quantity is a constant divided by the other quantity<\/dd>\n<\/dl>\n<\/section>\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-1494\">\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":5,"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-1494","chapter","type-chapter","status-publish","hentry"],"part":1485,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1494","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":3,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1494\/revisions"}],"predecessor-version":[{"id":2982,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1494\/revisions\/2982"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/1485"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1494\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/media?parent=1494"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1494"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/contributor?post=1494"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/license?post=1494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}