{"id":16508,"date":"2019-10-03T17:08:35","date_gmt":"2019-10-03T17:08:35","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/outcome-slope\/"},"modified":"2024-04-30T23:17:38","modified_gmt":"2024-04-30T23:17:38","slug":"outcome-slope","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/outcome-slope\/","title":{"raw":"Introduction to Finding Slope","rendered":"Introduction to Finding Slope"},"content":{"raw":"<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/05\/23183445\/cottage-768889_960_720.jpg\"><img class=\"aligncenter wp-image-13091\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/05\/23183445\/cottage-768889_960_720-300x198.jpg\" alt=\"A cottage roof\" width=\"703\" height=\"464\" \/><\/a>\r\n<h2>What you'll learn to do: Find the slope of a line<\/h2>\r\nVisual and verbal cues constantly give us information in our daily lives.\u00a0 For example, when you wake up in the morning and it is raining, you know that you'll want to find your umbrella. \u00a0Or when you order a vanilla spice latte and see the steam rising, you instinctively start to blow on it before you sip it.\u00a0 The slope of a line can provide the same kind of cues about what the line represents.\r\n\r\nSlope can describe a rapidly increasing trend, something that doesn't change over time, or a slowly decreasing amount. The beauty of the picture that the slope offers is that once you learn to interpret it, you can do so quickly without long sentences of explanation.\r\n\r\nThe steepness of the slant of a line is called the slope of the line.\u00a0 \u00a0As we\u2019ve been graphing linear equations, we\u2019ve seen that some lines slant up as they go from left to right and some lines slant down. Some lines are very steep and some lines are flatter. What determines whether a line slants up or down, and if its slant is steep or flat?\r\n\r\nThe concept of slope has many applications in the real world. The pitch of a roof and the grade of a highway or wheelchair ramp are just some examples in which you literally see slopes. And when you ride a bicycle, you feel the slope as you pump uphill or coast downhill.\r\n\r\nIn this section we will learn how to calculate the slope of a line, and how to interpret what kind of line is represented by different slopes - positive, negative, or zero.\r\n\r\nSpecifically, in this section you\u2019ll learn how to:\r\n<ul>\r\n \t<li>Find the slope of a line from its graph<\/li>\r\n \t<li>Find the slope of horizontal and vertical lines<\/li>\r\n \t<li>Use the slope formula to find the slope of a line between two points<\/li>\r\n<\/ul>\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)\r\n\r\n[ohm_question]146163[\/ohm_question]\r\n\r\nIf you missed this problem, review the following video.\r\n\r\nhttps:\/\/youtu.be\/eF_jiZvb79w\r\n\r\n2)\r\n\r\n[ohm_question]146485[\/ohm_question]\r\n\r\n3)\r\n\r\n[ohm_question]146487[\/ohm_question]\r\n\r\nIf you missed either of these problems, review the video below.\r\n\r\nhttps:\/\/youtu.be\/fcVnwjBgDmk\r\n\r\n4)\r\n\r\n[ohm_question]146162[\/ohm_question]\r\n\r\nIf you missed this problem, review this example.\r\n<div class=\"textbox shaded\">\r\n\r\nWhich of the following fractions are equivalent to [latex]\\Large\\frac{7}{-8}?[\/latex]\r\n\r\n[latex]\\Large\\frac{-7}{-8},\\frac{-7}{8},\\frac{7}{8},-\\frac{7}{8}[\/latex]\r\n[reveal-answer q=\"417548\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"417548\"]\r\n\r\nSolution:\r\nThe quotient of a positive and a negative is a negative, so [latex]\\Large\\frac{7}{-8}[\/latex] is negative. Of the fractions listed, [latex]\\Large\\frac{-7}{8}\\normalsize\\text{and}-\\Large\\frac{7}{8}[\/latex] are also negative.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>","rendered":"<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/05\/23183445\/cottage-768889_960_720.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-13091\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/05\/23183445\/cottage-768889_960_720-300x198.jpg\" alt=\"A cottage roof\" width=\"703\" height=\"464\" \/><\/a><\/p>\n<h2>What you&#8217;ll learn to do: Find the slope of a line<\/h2>\n<p>Visual and verbal cues constantly give us information in our daily lives.\u00a0 For example, when you wake up in the morning and it is raining, you know that you&#8217;ll want to find your umbrella. \u00a0Or when you order a vanilla spice latte and see the steam rising, you instinctively start to blow on it before you sip it.\u00a0 The slope of a line can provide the same kind of cues about what the line represents.<\/p>\n<p>Slope can describe a rapidly increasing trend, something that doesn&#8217;t change over time, or a slowly decreasing amount. The beauty of the picture that the slope offers is that once you learn to interpret it, you can do so quickly without long sentences of explanation.<\/p>\n<p>The steepness of the slant of a line is called the slope of the line.\u00a0 \u00a0As we\u2019ve been graphing linear equations, we\u2019ve seen that some lines slant up as they go from left to right and some lines slant down. Some lines are very steep and some lines are flatter. What determines whether a line slants up or down, and if its slant is steep or flat?<\/p>\n<p>The concept of slope has many applications in the real world. The pitch of a roof and the grade of a highway or wheelchair ramp are just some examples in which you literally see slopes. And when you ride a bicycle, you feel the slope as you pump uphill or coast downhill.<\/p>\n<p>In this section we will learn how to calculate the slope of a line, and how to interpret what kind of line is represented by different slopes &#8211; positive, negative, or zero.<\/p>\n<p>Specifically, in this section you\u2019ll learn how to:<\/p>\n<ul>\n<li>Find the slope of a line from its graph<\/li>\n<li>Find the slope of horizontal and vertical lines<\/li>\n<li>Use the slope formula to find the slope of a line between two points<\/li>\n<\/ul>\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)<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146163\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146163&theme=oea&iframe_resize_id=ohm146163&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=\"Simplify Basic Expressions in Fraction Form\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/eF_jiZvb79w?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>2)<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146485\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146485&theme=oea&iframe_resize_id=ohm146485&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>3)<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146487\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146487&theme=oea&iframe_resize_id=ohm146487&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed either of these problems, review the video below.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Multiplying and Dividing Involving Zero\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/fcVnwjBgDmk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>4)<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146162\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146162&theme=oea&iframe_resize_id=ohm146162&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\">\n<p>Which of the following fractions are equivalent to [latex]\\Large\\frac{7}{-8}?[\/latex]<\/p>\n<p>[latex]\\Large\\frac{-7}{-8},\\frac{-7}{8},\\frac{7}{8},-\\frac{7}{8}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q417548\">Show Solution<\/span><\/p>\n<div id=\"q417548\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nThe quotient of a positive and a negative is a negative, so [latex]\\Large\\frac{7}{-8}[\/latex] is negative. Of the fractions listed, [latex]\\Large\\frac{-7}{8}\\normalsize\\text{and}-\\Large\\frac{7}{8}[\/latex] are also negative.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":169554,"menu_order":8,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"012082040f0848959b64162572e7cb1a","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-16508","chapter","type-chapter","status-publish","hentry"],"part":8524,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16508","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/users\/169554"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16508\/revisions"}],"predecessor-version":[{"id":20480,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16508\/revisions\/20480"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/8524"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16508\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/media?parent=16508"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=16508"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=16508"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/license?post=16508"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}