{"id":10684,"date":"2017-06-05T14:59:59","date_gmt":"2017-06-05T14:59:59","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10684"},"modified":"2020-01-09T01:56:43","modified_gmt":"2020-01-09T01:56:43","slug":"summary-using-intercepts-to-plot-lines","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/chapter\/summary-using-intercepts-to-plot-lines\/","title":{"raw":"Summary: Plotting Lines on the Rectangular Coordinate System","rendered":"Summary: Plotting Lines on the Rectangular Coordinate System"},"content":{"raw":"<h1 style=\"text-align: center;\"><span style=\"color: #ff0000; background-color: #999999;\">End of textbook section. After reviewing the content below,\r\nClose this tab and proceed to the assignment\u00a0<\/span><\/h1>\r\n<h2 data-type=\"title\">Key Concepts<\/h2>\r\n<ul>\r\n \t<li><strong>Intercepts<\/strong>\r\n<ul id=\"eip-id1170325327811\">\r\n \t<li>The [latex]x[\/latex]-intercept is the point, [latex]\\left(a,0\\right)[\/latex] , where the graph crosses the [latex]x[\/latex]-axis. The [latex]x[\/latex]-intercept occurs when [latex]y[\/latex] is zero.<\/li>\r\n \t<li>The [latex]y[\/latex]-intercept is the point, [latex]\\left(0,b\\right)[\/latex] , where the graph crosses the [latex]y[\/latex]-axis. The [latex]y[\/latex]-intercept occurs when [latex]y[\/latex] is zero.<\/li>\r\n \t<li>The [latex]x[\/latex]-intercept occurs when [latex]y[\/latex] is zero.<\/li>\r\n \t<li>The [latex]y[\/latex]-intercept occurs when [latex]x[\/latex] is zero.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Find the <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em> intercepts from the equation of a line<\/strong>\r\n<ul id=\"eip-id1170322951803\">\r\n \t<li>To find the [latex]x[\/latex]-intercept of the line, let [latex]y=0[\/latex] and solve for [latex]x[\/latex].<\/li>\r\n \t<li>To find the [latex]y[\/latex]-intercept of the line, let [latex]x=0[\/latex] and solve for [latex]y[\/latex].\r\n<table id=\"eip-id1170320456586\" class=\"unnumbered\" summary=\"...\" data-label=\"\">\r\n<thead>\r\n<tr>\r\n<th>[latex]x[\/latex]<\/th>\r\n<th>[latex]y[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]0[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Graph a line using the intercepts<\/strong>\r\n<ol id=\"eip-id1170326539490\" class=\"stepwise\" data-number-style=\"arabic\">\r\n \t<li>Find the <em data-effect=\"italics\">x-<\/em> and <em data-effect=\"italics\">y-<\/em> intercepts of the line.\r\n<ul id=\"eip-id1170324213790\">\r\n \t<li>Let [latex]y=0[\/latex] and solve for [latex]x[\/latex].<\/li>\r\n \t<li>Let [latex]x=0[\/latex] and solve for [latex]y[\/latex].<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Find a third solution to the equation.<\/li>\r\n \t<li>Plot the three points and then check that they line up.<\/li>\r\n \t<li>Draw the line.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Choose the most convenient method to graph a line<\/strong><\/li>\r\n<\/ul>\r\n<ol id=\"eip-id1170323946856\" class=\"stepwise\" data-number-style=\"arabic\">\r\n \t<li>Determine if the equation has only one variable. Then it is a vertical or horizontal line.\r\n<ul>\r\n \t<li>[latex]x=a[\/latex] is a vertical line passing through the [latex]x[\/latex]-axis at [latex]a[\/latex].<\/li>\r\n \t<li>[latex]y=b[\/latex] is a vertical line passing through the [latex]y[\/latex]-axis at [latex]b[\/latex].<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Determine if y is isolated on one side of the equation. The graph by plotting points.Choose any three values for <em data-effect=\"italics\">x<\/em> and then solve for the corresponding <em data-effect=\"italics\">y-<\/em> values.<\/li>\r\n \t<li>Determine if the equation is of the form [latex]Ax+By=C[\/latex] , find the intercepts.Find the <em data-effect=\"italics\">x-<\/em> and <em data-effect=\"italics\">y-<\/em> intercepts and then a third point.<\/li>\r\n<\/ol>\r\n&nbsp;\r\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\r\n<dl id=\"fs-id1830018\" class=\"definition\">\r\n \t<dt>intercepts of a line<\/dt>\r\n \t<dd id=\"fs-id1830021\">Each of the points at which a line crosses the [latex]x[\/latex]-axis and the [latex]y[\/latex]-axis is called an intercept of the line.<\/dd>\r\n<\/dl>","rendered":"<h1 style=\"text-align: center;\"><span style=\"color: #ff0000; background-color: #999999;\">End of textbook section. After reviewing the content below,<br \/>\nClose this tab and proceed to the assignment\u00a0<\/span><\/h1>\n<h2 data-type=\"title\">Key Concepts<\/h2>\n<ul>\n<li><strong>Intercepts<\/strong>\n<ul id=\"eip-id1170325327811\">\n<li>The [latex]x[\/latex]-intercept is the point, [latex]\\left(a,0\\right)[\/latex] , where the graph crosses the [latex]x[\/latex]-axis. The [latex]x[\/latex]-intercept occurs when [latex]y[\/latex] is zero.<\/li>\n<li>The [latex]y[\/latex]-intercept is the point, [latex]\\left(0,b\\right)[\/latex] , where the graph crosses the [latex]y[\/latex]-axis. The [latex]y[\/latex]-intercept occurs when [latex]y[\/latex] is zero.<\/li>\n<li>The [latex]x[\/latex]-intercept occurs when [latex]y[\/latex] is zero.<\/li>\n<li>The [latex]y[\/latex]-intercept occurs when [latex]x[\/latex] is zero.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Find the <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em> intercepts from the equation of a line<\/strong>\n<ul id=\"eip-id1170322951803\">\n<li>To find the [latex]x[\/latex]-intercept of the line, let [latex]y=0[\/latex] and solve for [latex]x[\/latex].<\/li>\n<li>To find the [latex]y[\/latex]-intercept of the line, let [latex]x=0[\/latex] and solve for [latex]y[\/latex].<br \/>\n<table id=\"eip-id1170320456586\" class=\"unnumbered\" summary=\"...\" data-label=\"\">\n<thead>\n<tr>\n<th>[latex]x[\/latex]<\/th>\n<th>[latex]y[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]0[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]0[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ul>\n<\/li>\n<li><strong>Graph a line using the intercepts<\/strong>\n<ol id=\"eip-id1170326539490\" class=\"stepwise\" data-number-style=\"arabic\">\n<li>Find the <em data-effect=\"italics\">x-<\/em> and <em data-effect=\"italics\">y-<\/em> intercepts of the line.\n<ul id=\"eip-id1170324213790\">\n<li>Let [latex]y=0[\/latex] and solve for [latex]x[\/latex].<\/li>\n<li>Let [latex]x=0[\/latex] and solve for [latex]y[\/latex].<\/li>\n<\/ul>\n<\/li>\n<li>Find a third solution to the equation.<\/li>\n<li>Plot the three points and then check that they line up.<\/li>\n<li>Draw the line.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Choose the most convenient method to graph a line<\/strong><\/li>\n<\/ul>\n<ol id=\"eip-id1170323946856\" class=\"stepwise\" data-number-style=\"arabic\">\n<li>Determine if the equation has only one variable. Then it is a vertical or horizontal line.\n<ul>\n<li>[latex]x=a[\/latex] is a vertical line passing through the [latex]x[\/latex]-axis at [latex]a[\/latex].<\/li>\n<li>[latex]y=b[\/latex] is a vertical line passing through the [latex]y[\/latex]-axis at [latex]b[\/latex].<\/li>\n<\/ul>\n<\/li>\n<li>Determine if y is isolated on one side of the equation. The graph by plotting points.Choose any three values for <em data-effect=\"italics\">x<\/em> and then solve for the corresponding <em data-effect=\"italics\">y-<\/em> values.<\/li>\n<li>Determine if the equation is of the form [latex]Ax+By=C[\/latex] , find the intercepts.Find the <em data-effect=\"italics\">x-<\/em> and <em data-effect=\"italics\">y-<\/em> intercepts and then a third point.<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id1830018\" class=\"definition\">\n<dt>intercepts of a line<\/dt>\n<dd id=\"fs-id1830021\">Each of the points at which a line crosses the [latex]x[\/latex]-axis and the [latex]y[\/latex]-axis is called an intercept of the line.<\/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-10684\">\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":12,"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":"22e6b057-ede6-4386-bfc6-0fdf32a98dea","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-10684","chapter","type-chapter","status-publish","hentry"],"part":8524,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10684","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":11,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10684\/revisions"}],"predecessor-version":[{"id":16132,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10684\/revisions\/16132"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/parts\/8524"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10684\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/media?parent=10684"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=10684"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/contributor?post=10684"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/license?post=10684"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}