{"id":1748,"date":"2024-06-05T22:32:53","date_gmt":"2024-06-05T22:32:53","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=1748"},"modified":"2025-01-08T16:12:57","modified_gmt":"2025-01-08T16:12:57","slug":"graphs-of-linear-functions-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/graphs-of-linear-functions-apply-it-1\/","title":{"raw":"Graphs of Linear Functions: Apply It 1","rendered":"Graphs of Linear Functions: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Create and interpret equations of linear functions<\/li>\r\n \t<li>Identify and graph lines that are vertical or horizontal<\/li>\r\n \t<li>Graph straight lines by plotting points, using slope and y-intercept, and make changes like shifts to graphs<\/li>\r\n \t<li>Write equations for lines that run parallel or at a right angle to another line<\/li>\r\n<\/ul>\r\n<\/section>Linear equations show up everywhere, even in hands-on work like carpentry. When skilled carpenters like Kiran need to make precise cuts, they often use measurements and equations to ensure accuracy. Think of the cutting surface as a coordinate plane, where each point represents a specific position measured in inches. By writing these cuts as equations, Kiran can easily repeat the same cut on multiple boards without having to remeasure each time.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31789[\/ohm2_question]<\/section><section aria-label=\"Try It\">Let's start with a basic vertical cut. When carpenters make vertical cuts, the line runs straight up and down, parallel to the y-axis. Just like drawing a line on graph paper, we can describe this cut using a simple equation.<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31790[\/ohm2_question]<\/section><section aria-label=\"Try It\">Now let's look at horizontal cuts, which run parallel to the x-axis. These cuts are often used to trim boards to the right length or create level edges. Just like the vertical cut, we can represent these cuts with an equation.<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31791[\/ohm2_question]<\/section><section aria-label=\"Try It\">Now that we've mastered straight cuts, let's help Kiran with a more intricate design. Sometimes carpenters need to make a series of precise cuts to create decorative shapes or functional joints. Kiran wants to recreate a rhombus cut-out, which requires four carefully planned cuts that work together. Each cut will follow a specific line equation, and we need to find the exact endpoints to ensure the cuts meet perfectly.<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31792[\/ohm2_question]<\/section><section aria-label=\"Try It\">After completing the rhombus design, Kiran has another project that requires precise cuts: creating a square opening for a post to fit through. This is a common task in carpentry, like making a hole for a fence post or a support beam. Getting these cuts exactly right is crucial - if the opening is too small the post won't fit, and if it's too large, the post won't be secure.<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31793[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Create and interpret equations of linear functions<\/li>\n<li>Identify and graph lines that are vertical or horizontal<\/li>\n<li>Graph straight lines by plotting points, using slope and y-intercept, and make changes like shifts to graphs<\/li>\n<li>Write equations for lines that run parallel or at a right angle to another line<\/li>\n<\/ul>\n<\/section>\n<p>Linear equations show up everywhere, even in hands-on work like carpentry. When skilled carpenters like Kiran need to make precise cuts, they often use measurements and equations to ensure accuracy. Think of the cutting surface as a coordinate plane, where each point represents a specific position measured in inches. By writing these cuts as equations, Kiran can easily repeat the same cut on multiple boards without having to remeasure each time.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31789\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31789&theme=lumen&iframe_resize_id=ohm31789&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section aria-label=\"Try It\">Let&#8217;s start with a basic vertical cut. When carpenters make vertical cuts, the line runs straight up and down, parallel to the y-axis. Just like drawing a line on graph paper, we can describe this cut using a simple equation.<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31790\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31790&theme=lumen&iframe_resize_id=ohm31790&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section aria-label=\"Try It\">Now let&#8217;s look at horizontal cuts, which run parallel to the x-axis. These cuts are often used to trim boards to the right length or create level edges. Just like the vertical cut, we can represent these cuts with an equation.<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31791\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31791&theme=lumen&iframe_resize_id=ohm31791&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section aria-label=\"Try It\">Now that we&#8217;ve mastered straight cuts, let&#8217;s help Kiran with a more intricate design. Sometimes carpenters need to make a series of precise cuts to create decorative shapes or functional joints. Kiran wants to recreate a rhombus cut-out, which requires four carefully planned cuts that work together. Each cut will follow a specific line equation, and we need to find the exact endpoints to ensure the cuts meet perfectly.<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31792\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31792&theme=lumen&iframe_resize_id=ohm31792&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section aria-label=\"Try It\">After completing the rhombus design, Kiran has another project that requires precise cuts: creating a square opening for a post to fit through. This is a common task in carpentry, like making a hole for a fence post or a support beam. Getting these cuts exactly right is crucial &#8211; if the opening is too small the post won&#8217;t fit, and if it&#8217;s too large, the post won&#8217;t be secure.<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31793\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31793&theme=lumen&iframe_resize_id=ohm31793&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":12,"menu_order":18,"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":"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\/1748"}],"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":7,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1748\/revisions"}],"predecessor-version":[{"id":7126,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1748\/revisions\/7126"}],"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\/1748\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=1748"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1748"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=1748"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=1748"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}