{"id":16501,"date":"2019-10-03T17:08:31","date_gmt":"2019-10-03T17:08:31","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/outcome-graphing-linear-equations-3\/"},"modified":"2020-10-22T09:14:50","modified_gmt":"2020-10-22T09:14:50","slug":"outcome-graphing-linear-equations-3","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/outcome-graphing-linear-equations-3\/","title":{"raw":"9.1 - Introduction to The Coordinate Plane","rendered":"9.1 &#8211; Introduction to The Coordinate Plane"},"content":{"raw":"<h2>What you'll learn to do: Graph linear equations on the coordinate plane.<\/h2>\r\nThe <b>coordinate plane<\/b> was developed centuries ago (in 1637, to be exact) and refined by the French mathematician Ren\u00e9 Descartes. In his honor, the system is sometimes called the Cartesian coordinate system. The coordinate plane can be used to plot points and graph lines. This system allows us to describe algebraic relationships in a visual sense, and also helps us create and interpret algebraic concepts.\r\n\r\nSpecifically, in this section you\u2019ll learn how to:\r\n<ul>\r\n \t<li>Plot ordered pairs on a rectangular coordinate system<\/li>\r\n \t<li>Identify quadrants on the coordinate plane<\/li>\r\n \t<li>Identify points on a graph<\/li>\r\n \t<li>Determine when an ordered pair is a solution of an equation<\/li>\r\n \t<li>Complete a table of solutions to a linear equation<\/li>\r\n \t<li>Graph linear equations using ordered pairs<\/li>\r\n<\/ul>\r\n&nbsp;\r\n\r\nBefore you get started in this module, try a few practice problems and review\u00a0prior\u00a0concepts.\r\n<div class=\"textbox examples\">\r\n<h3>Readiness Quiz<\/h3>\r\n1)[ohm_question]144878[\/ohm_question]\r\n\r\nIf you missed this problem, review the example below.\r\n<div class=\"textbox shaded\">\r\n\r\nEvaluate [latex]x+7[\/latex] when\r\n<ol>\r\n \t<li>[latex]x=3[\/latex]<\/li>\r\n \t<li>[latex]x=12[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"528374\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"528374\"]\r\n\r\nSolution:\r\n\r\n1. To evaluate, substitute [latex]3[\/latex] for [latex]x[\/latex] in the expression, and then simplify.\r\n<table id=\"eip-id1166566546426\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression x plus 7. Substitute 3 for x. The expression becomes 3 plus x which is 10.\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]x+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute.<\/td>\r\n<td>[latex]\\color{red}{3}+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]10[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen [latex]x=3[\/latex], the expression [latex]x+7[\/latex] has a value of [latex]10[\/latex].\r\n2. To evaluate, substitute [latex]12[\/latex] for [latex]x[\/latex] in the expression, and then simplify.\r\n<table id=\"eip-id1166566410105\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression x plus 7, substitute 12 for x. The expression becomes 12 plus x which is 19.\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]x+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute.<\/td>\r\n<td>[latex]\\color{red}{12}+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]19[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen [latex]x=12[\/latex], the expression [latex]x+7[\/latex] has a value of [latex]19[\/latex].\r\n\r\nNotice that we got different results for parts 1 and 2 even though we started with the same expression. This is because the values used for [latex]x[\/latex] were different. When we evaluate an expression, the value varies depending on the value used for the variable.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n2)[ohm_question]144884[\/ohm_question]\r\n\r\nIf you missed this problem, review this example.\r\n<div class=\"textbox shaded\">[latex]\\text{Evaluate }3x+4y - 6\\text{ when }x=10\\text{ and }y=2[\/latex].\r\n[reveal-answer q=\"769566\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"769566\"]SolutionThis expression contains two variables, so we must make two substitutions.\r\n<table id=\"eip-id1168467158036\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression three x plus four y minus 6. Substitute 10 for x and 2 for y. The expression becomes 3 times 10 plus 4 times 2 minus 6. Perform multiplication from left to right. Three times 10 is 30 and 4 times 2 is 8. The expression becomes 30 plus 8 minus 6. Add and subtract from left to right. Thirty plus 8 is 38. Thirty-eight minus 6 is 32.\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3x+4y-6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]\\color{red}{10}[\/latex] for x and [latex]\\color{blue}{2}[\/latex] for y.<\/td>\r\n<td>[latex]3(\\color{red}{10})+4(\\color{blue}{2})-6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]30+8-6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add and subtract left to right.<\/td>\r\n<td>[latex]32[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen [latex]x=10[\/latex] and [latex]y=2[\/latex], the expression [latex]3x+4y - 6[\/latex] has a value of [latex]32[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n3)[ohm_question]142131[\/ohm_question]\r\n\r\nIf you missed this problem, review the following video.\r\n\r\nhttps:\/\/youtu.be\/_hBoWoctfAo\r\n\r\n<\/div>","rendered":"<h2>What you&#8217;ll learn to do: Graph linear equations on the coordinate plane.<\/h2>\n<p>The <b>coordinate plane<\/b> was developed centuries ago (in 1637, to be exact) and refined by the French mathematician Ren\u00e9 Descartes. In his honor, the system is sometimes called the Cartesian coordinate system. The coordinate plane can be used to plot points and graph lines. This system allows us to describe algebraic relationships in a visual sense, and also helps us create and interpret algebraic concepts.<\/p>\n<p>Specifically, in this section you\u2019ll learn how to:<\/p>\n<ul>\n<li>Plot ordered pairs on a rectangular coordinate system<\/li>\n<li>Identify quadrants on the coordinate plane<\/li>\n<li>Identify points on a graph<\/li>\n<li>Determine when an ordered pair is a solution of an equation<\/li>\n<li>Complete a table of solutions to a linear equation<\/li>\n<li>Graph linear equations using ordered pairs<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p>Before you get started in this module, try a few practice problems and review\u00a0prior\u00a0concepts.<\/p>\n<div class=\"textbox examples\">\n<h3>Readiness Quiz<\/h3>\n<p>1)<iframe loading=\"lazy\" id=\"ohm144878\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144878&theme=oea&iframe_resize_id=ohm144878&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed this problem, review the example below.<\/p>\n<div class=\"textbox shaded\">\n<p>Evaluate [latex]x+7[\/latex] when<\/p>\n<ol>\n<li>[latex]x=3[\/latex]<\/li>\n<li>[latex]x=12[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q528374\">Show Solution<\/span><\/p>\n<div id=\"q528374\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<p>1. To evaluate, substitute [latex]3[\/latex] for [latex]x[\/latex] in the expression, and then simplify.<\/p>\n<table id=\"eip-id1166566546426\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression x plus 7. Substitute 3 for x. The expression becomes 3 plus x which is 10.\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]x+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute.<\/td>\n<td>[latex]\\color{red}{3}+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]10[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When [latex]x=3[\/latex], the expression [latex]x+7[\/latex] has a value of [latex]10[\/latex].<br \/>\n2. To evaluate, substitute [latex]12[\/latex] for [latex]x[\/latex] in the expression, and then simplify.<\/p>\n<table id=\"eip-id1166566410105\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression x plus 7, substitute 12 for x. The expression becomes 12 plus x which is 19.\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]x+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute.<\/td>\n<td>[latex]\\color{red}{12}+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]19[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When [latex]x=12[\/latex], the expression [latex]x+7[\/latex] has a value of [latex]19[\/latex].<\/p>\n<p>Notice that we got different results for parts 1 and 2 even though we started with the same expression. This is because the values used for [latex]x[\/latex] were different. When we evaluate an expression, the value varies depending on the value used for the variable.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>2)<iframe loading=\"lazy\" id=\"ohm144884\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144884&theme=oea&iframe_resize_id=ohm144884&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed this problem, review this example.<\/p>\n<div class=\"textbox shaded\">[latex]\\text{Evaluate }3x+4y - 6\\text{ when }x=10\\text{ and }y=2[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q769566\">Show Solution<\/span><\/p>\n<div id=\"q769566\" class=\"hidden-answer\" style=\"display: none\">SolutionThis expression contains two variables, so we must make two substitutions.<\/p>\n<table id=\"eip-id1168467158036\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression three x plus four y minus 6. Substitute 10 for x and 2 for y. The expression becomes 3 times 10 plus 4 times 2 minus 6. Perform multiplication from left to right. Three times 10 is 30 and 4 times 2 is 8. The expression becomes 30 plus 8 minus 6. Add and subtract from left to right. Thirty plus 8 is 38. Thirty-eight minus 6 is 32.\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]3x+4y-6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{10}[\/latex] for x and [latex]\\color{blue}{2}[\/latex] for y.<\/td>\n<td>[latex]3(\\color{red}{10})+4(\\color{blue}{2})-6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]30+8-6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add and subtract left to right.<\/td>\n<td>[latex]32[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When [latex]x=10[\/latex] and [latex]y=2[\/latex], the expression [latex]3x+4y - 6[\/latex] has a value of [latex]32[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>3)<iframe loading=\"lazy\" id=\"ohm142131\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142131&theme=oea&iframe_resize_id=ohm142131&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed this problem, review the following video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Solve a Linear Equation in One Variable with Variables on Both Sides: 2x+8=-2x-24\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/_hBoWoctfAo?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\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-16501\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Authored by<\/strong>: Quadrants on the Coordinate Plane. <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":169554,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"Quadrants on the Coordinate Plane\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"04dcacf26ac2496eb29551e7708e024a","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-16501","chapter","type-chapter","status-publish","hentry"],"part":8524,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16501","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/users\/169554"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16501\/revisions"}],"predecessor-version":[{"id":20327,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16501\/revisions\/20327"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/8524"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16501\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/media?parent=16501"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=16501"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=16501"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/license?post=16501"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}