{"id":790,"date":"2025-07-15T16:31:56","date_gmt":"2025-07-15T16:31:56","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=790"},"modified":"2026-01-12T16:13:29","modified_gmt":"2026-01-12T16:13:29","slug":"linear-functions-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/linear-functions-apply-it\/","title":{"raw":"Linear Functions: Apply It","rendered":"Linear Functions: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Write the equation of a linear function given a point and a slope, two points, or a table of values.<\/li>\r\n \t<li>Graph linear functions given any form of its equation.<\/li>\r\n \t<li>Graph and write the equations of horizontal and vertical lines.<\/li>\r\n \t<li>Write the equation of a line parallel or perpendicular to a given 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\">[ohm_question hide_question_numbers=1]318750[\/ohm_question]<\/section>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.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]318750[\/ohm_question]<\/section>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.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]318751[\/ohm_question]<\/section>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.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]318752[\/ohm_question]<\/section>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.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]318753[\/ohm_question]<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Write the equation of a linear function given a point and a slope, two points, or a table of values.<\/li>\n<li>Graph linear functions given any form of its equation.<\/li>\n<li>Graph and write the equations of horizontal and vertical lines.<\/li>\n<li>Write the equation of a line parallel or perpendicular to a given 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=\"ohm318750\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=318750&theme=lumen&iframe_resize_id=ohm318750&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>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.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm318750\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=318750&theme=lumen&iframe_resize_id=ohm318750&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>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.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm318751\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=318751&theme=lumen&iframe_resize_id=ohm318751&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>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.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm318752\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=318752&theme=lumen&iframe_resize_id=ohm318752&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>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.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm318753\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=318753&theme=lumen&iframe_resize_id=ohm318753&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":13,"menu_order":21,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":61,"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\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/790"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/13"}],"version-history":[{"count":5,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/790\/revisions"}],"predecessor-version":[{"id":5275,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/790\/revisions\/5275"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/61"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/790\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=790"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=790"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=790"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=790"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}