{"id":1679,"date":"2024-06-03T18:49:36","date_gmt":"2024-06-03T18:49:36","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=1679"},"modified":"2025-08-13T23:19:18","modified_gmt":"2025-08-13T23:19:18","slug":"module-7-background-youll-need-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/module-7-background-youll-need-3\/","title":{"raw":"Linear Functions: Background You'll Need 3","rendered":"Linear Functions: Background You&#8217;ll Need 3"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Plot points on the Cartesian coordinate plane.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>The Cartesian Coordinate Plane<\/h2>\r\nThe Cartesian coordinate system, also called the rectangular coordinate system, is based on a two-dimensional plane consisting of the\u00a0[latex]x[\/latex]-axis and the\u00a0[latex]y[\/latex]-axis. Perpendicular to each other, the axes divide the plane into four sections. Each section is called a\u00a0<strong>quadrant<\/strong>; the quadrants are numbered counterclockwise as shown in the figure below.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"487\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/12042358\/CNX_CAT_Figure_02_01_002.jpg\" alt=\"This is an image of an x, y plane with the axes labeled. The upper right section is labeled: Quadrant I. The upper left section is labeled: Quadrant II. The lower left section is labeled: Quadrant III. The lower right section is labeled: Quadrant IV.\" width=\"487\" height=\"442\" \/> <b>The Cartesian coordinate system with all four quadrants labeled.<\/b>[\/caption]\r\n\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]23247[\/ohm2_question]<\/section>Each point in the plane is identified by its <strong>[latex]x[\/latex]<em>-<\/em>coordinate<\/strong>,\u00a0or horizontal displacement from the origin, and its <strong>[latex]y[\/latex]<em>-<\/em>coordinate<\/strong>, or vertical displacement from the origin. Together we write them as an <strong>ordered pair<\/strong> indicating the combined distance from the origin in the form [latex]\\left(x,y\\right)[\/latex]. An ordered pair is also known as a coordinate pair because it consists of [latex]x[\/latex]and [latex]y[\/latex]-coordinates.\r\n\r\nFor example: The center of the plane is the point at which the two axes cross. It is known as the <strong>origin\u00a0<\/strong>or point [latex]\\left(0,0\\right)[\/latex].\r\n\r\n<section class=\"textbox example\">Represent the point [latex]\\left(3,-1\\right)[\/latex] in the coordinate plane.[reveal-answer q=\"411575\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"411575\"]We can represent the point [latex]\\left(3,-1\\right)[\/latex] in the plane by moving three units to the right of the origin in the horizontal direction and one unit down in the vertical direction.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"358\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/12042403\/CNX_CAT_Figure_02_01_004.jpg\" alt=\"This is an image of an x, y coordinate plane. The x and y axis range from negative 5 to 5. The point (3, -1) is labeled. An arrow extends rightward from the origin 3 units and another arrow extends downward one unit from the end of that arrow to the point.\" width=\"358\" height=\"325\" \/> x,y coordinate plane with the point (3,-1) labeled[\/caption]\r\n\r\n[\/hidden-answer]<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]23248[\/ohm2_question]<\/section><section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]23249[\/ohm2_question]<\/section><\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Plot points on the Cartesian coordinate plane.<\/li>\n<\/ul>\n<\/section>\n<h2>The Cartesian Coordinate Plane<\/h2>\n<p>The Cartesian coordinate system, also called the rectangular coordinate system, is based on a two-dimensional plane consisting of the\u00a0[latex]x[\/latex]-axis and the\u00a0[latex]y[\/latex]-axis. Perpendicular to each other, the axes divide the plane into four sections. Each section is called a\u00a0<strong>quadrant<\/strong>; the quadrants are numbered counterclockwise as shown in the figure below.<\/p>\n<figure style=\"width: 487px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/12042358\/CNX_CAT_Figure_02_01_002.jpg\" alt=\"This is an image of an x, y plane with the axes labeled. The upper right section is labeled: Quadrant I. The upper left section is labeled: Quadrant II. The lower left section is labeled: Quadrant III. The lower right section is labeled: Quadrant IV.\" width=\"487\" height=\"442\" \/><figcaption class=\"wp-caption-text\"><b>The Cartesian coordinate system with all four quadrants labeled.<\/b><\/figcaption><\/figure>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm23247\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=23247&theme=lumen&iframe_resize_id=ohm23247&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Each point in the plane is identified by its <strong>[latex]x[\/latex]<em>&#8211;<\/em>coordinate<\/strong>,\u00a0or horizontal displacement from the origin, and its <strong>[latex]y[\/latex]<em>&#8211;<\/em>coordinate<\/strong>, or vertical displacement from the origin. Together we write them as an <strong>ordered pair<\/strong> indicating the combined distance from the origin in the form [latex]\\left(x,y\\right)[\/latex]. An ordered pair is also known as a coordinate pair because it consists of [latex]x[\/latex]and [latex]y[\/latex]-coordinates.<\/p>\n<p>For example: The center of the plane is the point at which the two axes cross. It is known as the <strong>origin\u00a0<\/strong>or point [latex]\\left(0,0\\right)[\/latex].<\/p>\n<section class=\"textbox example\">Represent the point [latex]\\left(3,-1\\right)[\/latex] in the coordinate plane.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q411575\">Show Answer<\/button><\/p>\n<div id=\"q411575\" class=\"hidden-answer\" style=\"display: none\">We can represent the point [latex]\\left(3,-1\\right)[\/latex] in the plane by moving three units to the right of the origin in the horizontal direction and one unit down in the vertical direction.<\/p>\n<figure style=\"width: 358px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/12042403\/CNX_CAT_Figure_02_01_004.jpg\" alt=\"This is an image of an x, y coordinate plane. The x and y axis range from negative 5 to 5. The point (3, -1) is labeled. An arrow extends rightward from the origin 3 units and another arrow extends downward one unit from the end of that arrow to the point.\" width=\"358\" height=\"325\" \/><figcaption class=\"wp-caption-text\">x,y coordinate plane with the point (3,-1) labeled<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm23248\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=23248&theme=lumen&iframe_resize_id=ohm23248&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm23249\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=23249&theme=lumen&iframe_resize_id=ohm23249&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n","protected":false},"author":12,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":164,"module-header":"background_you_need","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1679"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":10,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1679\/revisions"}],"predecessor-version":[{"id":3959,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1679\/revisions\/3959"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/parts\/164"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1679\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=1679"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1679"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=1679"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=1679"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}