{"id":1014,"date":"2024-05-01T21:51:32","date_gmt":"2024-05-01T21:51:32","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=1014"},"modified":"2025-08-13T15:20:09","modified_gmt":"2025-08-13T15:20:09","slug":"graphing-and-analyzing-linear-equations-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/graphing-and-analyzing-linear-equations-apply-it-1\/","title":{"raw":"Graphing and Analyzing Linear Equations: Apply It 1","rendered":"Graphing and Analyzing Linear Equations: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Learn to plot points and draw lines on a graph using a set of coordinates.<\/li>\r\n \t<li>Find the x-intercept and y-intercept of graphs.<\/li>\r\n \t<li>Determine the slope based on the steepness and direction of a line.<\/li>\r\n \t<li>Use formulas to calculate the distances and midpoints between points.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Loading Dock Safety: Analyzing Ramp Slopes<\/h2>\r\nThe safety specifications for a semi-truck loading ramp can be modeled by the linear equation [latex]y = (-\\frac{1}{4})x + 4.25[\/latex], where [latex]x[\/latex] represents the horizontal distance in feet from the back of the truck, and [latex]y[\/latex] represents the height of the ramp in feet above the ground. For practical purposes, we'll focus on the portion of the graph in Quadrant I, where both [latex]x[\/latex] and [latex]y[\/latex] are positive.\r\n\r\n[caption id=\"attachment_6785\" align=\"aligncenter\" width=\"502\"]<img class=\"wp-image-6785 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/17145059\/large-3.1.A.Diagram1.png\" alt=\"The image shows a coordinate plane with arrows extending along both the x and y axes. On the left side of the y-axis, there is a simple gray silhouette of a delivery truck or van. From the back of the truck, a thin blue line extends downward and to the right, creating a negative slope that continues to the edge of the image.\" width=\"502\" height=\"254\" \/> Truck with downward-sloping line in a coordinate plane[\/caption]\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]26835[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]26836[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]26838[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]26839[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]26840[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]26846[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]26847[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]26848[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Learn to plot points and draw lines on a graph using a set of coordinates.<\/li>\n<li>Find the x-intercept and y-intercept of graphs.<\/li>\n<li>Determine the slope based on the steepness and direction of a line.<\/li>\n<li>Use formulas to calculate the distances and midpoints between points.<\/li>\n<\/ul>\n<\/section>\n<h2>Loading Dock Safety: Analyzing Ramp Slopes<\/h2>\n<p>The safety specifications for a semi-truck loading ramp can be modeled by the linear equation [latex]y = (-\\frac{1}{4})x + 4.25[\/latex], where [latex]x[\/latex] represents the horizontal distance in feet from the back of the truck, and [latex]y[\/latex] represents the height of the ramp in feet above the ground. For practical purposes, we&#8217;ll focus on the portion of the graph in Quadrant I, where both [latex]x[\/latex] and [latex]y[\/latex] are positive.<\/p>\n<figure id=\"attachment_6785\" aria-describedby=\"caption-attachment-6785\" style=\"width: 502px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6785 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/17145059\/large-3.1.A.Diagram1.png\" alt=\"The image shows a coordinate plane with arrows extending along both the x and y axes. On the left side of the y-axis, there is a simple gray silhouette of a delivery truck or van. From the back of the truck, a thin blue line extends downward and to the right, creating a negative slope that continues to the edge of the image.\" width=\"502\" height=\"254\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/17145059\/large-3.1.A.Diagram1.png 502w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/17145059\/large-3.1.A.Diagram1-300x152.png 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/17145059\/large-3.1.A.Diagram1-65x33.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/17145059\/large-3.1.A.Diagram1-225x114.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/17145059\/large-3.1.A.Diagram1-350x177.png 350w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><figcaption id=\"caption-attachment-6785\" class=\"wp-caption-text\">Truck with downward-sloping line in a coordinate plane<\/figcaption><\/figure>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm26835\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=26835&theme=lumen&iframe_resize_id=ohm26835&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm26836\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=26836&theme=lumen&iframe_resize_id=ohm26836&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm26838\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=26838&theme=lumen&iframe_resize_id=ohm26838&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm26839\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=26839&theme=lumen&iframe_resize_id=ohm26839&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm26840\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=26840&theme=lumen&iframe_resize_id=ohm26840&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm26846\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=26846&theme=lumen&iframe_resize_id=ohm26846&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm26847\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=26847&theme=lumen&iframe_resize_id=ohm26847&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm26848\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=26848&theme=lumen&iframe_resize_id=ohm26848&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":12,"menu_order":10,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":75,"module-header":"apply_it","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\/1014"}],"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":17,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1014\/revisions"}],"predecessor-version":[{"id":7589,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1014\/revisions\/7589"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/parts\/75"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1014\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=1014"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1014"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=1014"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=1014"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}