{"id":10675,"date":"2017-06-05T14:58:19","date_gmt":"2017-06-05T14:58:19","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10675"},"modified":"2020-10-22T09:15:47","modified_gmt":"2020-10-22T09:15:47","slug":"summary-plotting-points-and-lines-on-the-rectangular-coordinate-system","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/summary-plotting-points-and-lines-on-the-rectangular-coordinate-system\/","title":{"raw":"9.1.e - Summary: The Coordinate Plane","rendered":"9.1.e &#8211; Summary: The Coordinate Plane"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul id=\"eip-87\">\r\n \t<li><strong>Ordered Pair<\/strong>\u00a0 An ordered pair, [latex]\\left(x,y\\right)[\/latex] gives the coordinates of a point in a rectangular coordinate system.[latex]\\begin{array}{c}\\text{The first number is the }x\\text{-coordinate}.\\hfill \\\\ \\text{The second number is the }y\\text{-coordinate}.\\hfill \\end{array}[\/latex]<\/li>\r\n \t<li><strong>Steps for Plotting an Ordered Pair (<i>x<\/i>, <i>y<\/i>) in the Coordinate Plane<\/strong>\r\n<ul>\r\n \t<li>Determine the <i>x-<\/i>coordinate. Beginning at the origin, move horizontally, the direction of the <i>x<\/i>-axis, the distance given by the <i>x-<\/i>coordinate. If the <i>x-<\/i>coordinate is positive, move to the right; if the <i>x-<\/i>coordinate is negative, move to the left.<\/li>\r\n \t<li>Determine the <i>y-<\/i>coordinate. Beginning at the <i>x-<\/i>coordinate, move vertically, the direction of the <i>y<\/i>-axis, the distance given by the <i>y-<\/i>coordinate. If the <i>y-<\/i>coordinate is positive, move up; if the <i>y-<\/i>coordinate is negative, move down.<\/li>\r\n \t<li>Draw a point at the ending location. Label the point with the ordered pair.<\/li>\r\n \t<li>An ordered pair is represented by a <strong>single<\/strong> point on the graph.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Sign Patterns of the Quadrants<\/strong>\r\n<table id=\"eip-id1170324021306\" class=\"unnumbered unstyled\" summary=\"...\">\r\n<thead>\r\n<tr>\r\n<th>Quadrant I<\/th>\r\n<th>Quadrant II<\/th>\r\n<th>Quadrant III<\/th>\r\n<th>Quadrant IV<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex](x,y)[\/latex]<\/td>\r\n<td>[latex](x,y)[\/latex]<\/td>\r\n<td>[latex](x,y)[\/latex]<\/td>\r\n<td>[latex](x,y)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex](+,+)[\/latex]<\/td>\r\n<td>[latex](\u2212,+)[\/latex]<\/td>\r\n<td>[latex](\u2212,\u2212)[\/latex]<\/td>\r\n<td>[latex](+,\u2212)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t<li><strong>Coordinates of Zero<\/strong>\r\n<ul id=\"eip-id1170325448704\">\r\n \t<li>Points with a [latex]y[\/latex]-coordinate equal to [latex]0[\/latex] are on the <em>x-<\/em>axis, and have coordinates [latex] (a, 0)[\/latex].<\/li>\r\n \t<li>Points with a [latex]x[\/latex]-coordinate equal to [latex]0[\/latex] are on the <em>y-<\/em>axis, and have coordinates [latex](0, b)[\/latex].<\/li>\r\n \t<li>The point [latex](0, 0)[\/latex] is called the origin. It is the point where the <em>x-<\/em>axis and <em>y-<\/em>axis intersect.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>\r\n<p id=\"Identifying Solutions\"><strong>Identifying Solutions\u00a0\u00a0<\/strong>To find out whether an ordered pair is a solution of a linear equation, you can do the following:<\/p>\r\n\r\n<ul>\r\n \t<li>Graph the linear equation, and graph the ordered pair. If the ordered pair appears to be on the graph of a line, then it is a possible solution of the linear equation. If the ordered pair does not lie on the graph of a line, then it is not a solution.<\/li>\r\n \t<li>Substitute the (<i>x<\/i>, <i>y<\/i>) values into the equation. If the equation yields a true statement, then the ordered pair is a solution of the linear equation. If the ordered pair does not yield a true statement then it is not a solution.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<dl id=\"fs-id1610827\" class=\"definition\">\r\n \t<dt>linear equation<\/dt>\r\n \t<dd id=\"fs-id1610832\">An equation of the form [latex]Ax+By=C[\/latex], where [latex]A[\/latex] and [latex]B[\/latex] are not both zero, is called a linear equation in two variables.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id161087889\" class=\"definition\">\r\n \t<dt>ordered pair<\/dt>\r\n \t<dd id=\"fs-id1610884\">An ordered pair [latex]\\left(x,y\\right)[\/latex] gives the coordinates of a point in a rectangular coordinate system. The first number is the [latex]x[\/latex] -coordinate. The second number is the [latex]y[\/latex] -coordinate.\r\n\r\n[latex]\\underset{x\\text{-coordinate},y\\text{-coordinate}}{\\left(x,y\\right)}[\/latex]<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1610891\" class=\"definition\">\r\n \t<dt>origin<\/dt>\r\n \t<dd id=\"fs-id1610896\">The point [latex]\\left(0,0\\right)[\/latex] is called the origin. It is the point where the the point where the [latex]x[\/latex] -axis and [latex]y[\/latex] -axis intersect.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1610937\" class=\"definition\">\r\n \t<dt>quadrants<\/dt>\r\n \t<dd id=\"fs-id1610942\">The [latex]x[\/latex] -axis and [latex]y[\/latex] -axis divide a rectangular coordinate system into four areas, called quadrants.\u00a0 The quadrants are labeled with the Roman Numerals I, II, III, IV going around the coordinate system in a counter-clockwise direction.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1610946\" class=\"definition\">\r\n \t<dt>solution to a linear equation in two variables<\/dt>\r\n \t<dd id=\"fs-id1610952\">An ordered pair [latex]\\left(x,y\\right)[\/latex] is a solution to the linear equation [latex]Ax+By=C[\/latex], if the equation is a true statement when the <em>x-<\/em> and <em>y<\/em>-values of the ordered pair are substituted into the equation.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1610956\" class=\"definition\">\r\n \t<dt><em>x<\/em>-axis<\/dt>\r\n \t<dd id=\"fs-id1610966\">The <em>x<\/em>-axis is the horizontal axis in a rectangular coordinate system.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1610970\" class=\"definition\">\r\n \t<dt><em>y<\/em>-axis<\/dt>\r\n \t<dd id=\"fs-id1610980\">The <em>y<\/em>-axis is the vertical axis on a rectangular coordinate system.<\/dd>\r\n<\/dl>","rendered":"<h2>Key Concepts<\/h2>\n<ul id=\"eip-87\">\n<li><strong>Ordered Pair<\/strong>\u00a0 An ordered pair, [latex]\\left(x,y\\right)[\/latex] gives the coordinates of a point in a rectangular coordinate system.[latex]\\begin{array}{c}\\text{The first number is the }x\\text{-coordinate}.\\hfill \\\\ \\text{The second number is the }y\\text{-coordinate}.\\hfill \\end{array}[\/latex]<\/li>\n<li><strong>Steps for Plotting an Ordered Pair (<i>x<\/i>, <i>y<\/i>) in the Coordinate Plane<\/strong>\n<ul>\n<li>Determine the <i>x-<\/i>coordinate. Beginning at the origin, move horizontally, the direction of the <i>x<\/i>-axis, the distance given by the <i>x-<\/i>coordinate. If the <i>x-<\/i>coordinate is positive, move to the right; if the <i>x-<\/i>coordinate is negative, move to the left.<\/li>\n<li>Determine the <i>y-<\/i>coordinate. Beginning at the <i>x-<\/i>coordinate, move vertically, the direction of the <i>y<\/i>-axis, the distance given by the <i>y-<\/i>coordinate. If the <i>y-<\/i>coordinate is positive, move up; if the <i>y-<\/i>coordinate is negative, move down.<\/li>\n<li>Draw a point at the ending location. Label the point with the ordered pair.<\/li>\n<li>An ordered pair is represented by a <strong>single<\/strong> point on the graph.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Sign Patterns of the Quadrants<\/strong><br \/>\n<table id=\"eip-id1170324021306\" class=\"unnumbered unstyled\" summary=\"...\">\n<thead>\n<tr>\n<th>Quadrant I<\/th>\n<th>Quadrant II<\/th>\n<th>Quadrant III<\/th>\n<th>Quadrant IV<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex](x,y)[\/latex]<\/td>\n<td>[latex](x,y)[\/latex]<\/td>\n<td>[latex](x,y)[\/latex]<\/td>\n<td>[latex](x,y)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex](+,+)[\/latex]<\/td>\n<td>[latex](\u2212,+)[\/latex]<\/td>\n<td>[latex](\u2212,\u2212)[\/latex]<\/td>\n<td>[latex](+,\u2212)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li><strong>Coordinates of Zero<\/strong>\n<ul id=\"eip-id1170325448704\">\n<li>Points with a [latex]y[\/latex]-coordinate equal to [latex]0[\/latex] are on the <em>x-<\/em>axis, and have coordinates [latex](a, 0)[\/latex].<\/li>\n<li>Points with a [latex]x[\/latex]-coordinate equal to [latex]0[\/latex] are on the <em>y-<\/em>axis, and have coordinates [latex](0, b)[\/latex].<\/li>\n<li>The point [latex](0, 0)[\/latex] is called the origin. It is the point where the <em>x-<\/em>axis and <em>y-<\/em>axis intersect.<\/li>\n<\/ul>\n<\/li>\n<li>\n<p id=\"Identifying Solutions\"><strong>Identifying Solutions\u00a0\u00a0<\/strong>To find out whether an ordered pair is a solution of a linear equation, you can do the following:<\/p>\n<ul>\n<li>Graph the linear equation, and graph the ordered pair. If the ordered pair appears to be on the graph of a line, then it is a possible solution of the linear equation. If the ordered pair does not lie on the graph of a line, then it is not a solution.<\/li>\n<li>Substitute the (<i>x<\/i>, <i>y<\/i>) values into the equation. If the equation yields a true statement, then the ordered pair is a solution of the linear equation. If the ordered pair does not yield a true statement then it is not a solution.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1610827\" class=\"definition\">\n<dt>linear equation<\/dt>\n<dd id=\"fs-id1610832\">An equation of the form [latex]Ax+By=C[\/latex], where [latex]A[\/latex] and [latex]B[\/latex] are not both zero, is called a linear equation in two variables.<\/dd>\n<\/dl>\n<dl id=\"fs-id161087889\" class=\"definition\">\n<dt>ordered pair<\/dt>\n<dd id=\"fs-id1610884\">An ordered pair [latex]\\left(x,y\\right)[\/latex] gives the coordinates of a point in a rectangular coordinate system. The first number is the [latex]x[\/latex] -coordinate. The second number is the [latex]y[\/latex] -coordinate.<\/p>\n<p>[latex]\\underset{x\\text{-coordinate},y\\text{-coordinate}}{\\left(x,y\\right)}[\/latex]<\/dd>\n<\/dl>\n<dl id=\"fs-id1610891\" class=\"definition\">\n<dt>origin<\/dt>\n<dd id=\"fs-id1610896\">The point [latex]\\left(0,0\\right)[\/latex] is called the origin. It is the point where the the point where the [latex]x[\/latex] -axis and [latex]y[\/latex] -axis intersect.<\/dd>\n<\/dl>\n<dl id=\"fs-id1610937\" class=\"definition\">\n<dt>quadrants<\/dt>\n<dd id=\"fs-id1610942\">The [latex]x[\/latex] -axis and [latex]y[\/latex] -axis divide a rectangular coordinate system into four areas, called quadrants.\u00a0 The quadrants are labeled with the Roman Numerals I, II, III, IV going around the coordinate system in a counter-clockwise direction.<\/dd>\n<\/dl>\n<dl id=\"fs-id1610946\" class=\"definition\">\n<dt>solution to a linear equation in two variables<\/dt>\n<dd id=\"fs-id1610952\">An ordered pair [latex]\\left(x,y\\right)[\/latex] is a solution to the linear equation [latex]Ax+By=C[\/latex], if the equation is a true statement when the <em>x-<\/em> and <em>y<\/em>-values of the ordered pair are substituted into the equation.<\/dd>\n<\/dl>\n<dl id=\"fs-id1610956\" class=\"definition\">\n<dt><em>x<\/em>-axis<\/dt>\n<dd id=\"fs-id1610966\">The <em>x<\/em>-axis is the horizontal axis in a rectangular coordinate system.<\/dd>\n<\/dl>\n<dl id=\"fs-id1610970\" class=\"definition\">\n<dt><em>y<\/em>-axis<\/dt>\n<dd id=\"fs-id1610980\">The <em>y<\/em>-axis is the vertical axis on a rectangular coordinate system.<\/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-10675\">\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":7,"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":"04dcacf26ac2496eb29551e7708e024a","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-10675","chapter","type-chapter","status-publish","hentry"],"part":8524,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10675","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\/17533"}],"version-history":[{"count":15,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10675\/revisions"}],"predecessor-version":[{"id":20332,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10675\/revisions\/20332"}],"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\/10675\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/media?parent=10675"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=10675"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=10675"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/license?post=10675"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}