{"id":1060,"date":"2024-05-02T22:43:46","date_gmt":"2024-05-02T22:43:46","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=1060"},"modified":"2025-08-21T23:13:11","modified_gmt":"2025-08-21T23:13:11","slug":"equations-of-lines-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/equations-of-lines-apply-it-1\/","title":{"raw":"Equations of Lines: Apply It 1","rendered":"Equations of Lines: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Find the value of a variable that satisfies an equation<\/li>\r\n \t<li>Write equations for lines using different forms: slope-intercept, point-slope, and standard form<\/li>\r\n \t<li>Recognize and write equations for horizontal and vertical lines<\/li>\r\n \t<li>Determine if lines are parallel or perpendicular, and write equations for lines parallel or perpendicular to a given line<\/li>\r\n<\/ul>\r\n<\/section>The chief financial officer, or CFO, of a company is in charge of financial planning, risk management, budgeting, record keeping, and reporting. Dhakiya is the CFO of a non-profit community arts center.\r\n\r\nOne of Dhakiya\u2019s responsibilities is to track the sales of fundraising merchandise. She is hoping to raise [latex]$2000[\/latex] in the month of February with sales of merchandise averaging [latex]$75[\/latex] a day. If [latex]y[\/latex] represents the total money raised in [latex]x[\/latex] days of sales, Dhakiya can use a linear equation to model the fundraiser.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]26849[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]26850[\/ohm2_question]<\/section>The fundraising merchandise was created by volunteers using mostly repurposed or donated materials. This way, Dhakiya was able to keep the overhead costs for this fundraiser fairly low. The [latex]y[\/latex]-intercept indicates the overhead cost of materials for the merchandise that will be deducted from the total sales.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]26851[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]26852[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]26853[\/ohm2_question]<\/section>Another one of Dhakiya\u2019s responsibilities is applying for grants to fund activities for the youth programs at the community arts center. Dhakiya is applying to two grants that each offer a starting amount and additional funds based on the number of participants in the youth programs. The following equations represent the total funding provided, [latex]y[\/latex], given [latex]x[\/latex] participants in the youth programs.\r\n<ul>\r\n \t<li>Grant 1: [latex]y=40(x+25)[\/latex]<\/li>\r\n \t<li>Grant 2: [latex]-80x+2y=1600[\/latex]<\/li>\r\n<\/ul>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31609[\/ohm2_question]<\/section>\r\n\r\n[caption id=\"attachment_6725\" align=\"aligncenter\" width=\"200\"]<img class=\"wp-image-6725 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16034058\/blue_clay_3.2-Equations-of-Lines-200x300.jpg\" alt=\"\" width=\"200\" height=\"300\" \/> Clay workshop. Photo by Annie Spratt on Unsplash[\/caption]\r\n\r\nAfter analyzing the community art center\u2019s energy bills, Dhakiya determined the best plan for the polymer clay workshops that conserves energy. Ovens are used to bake the sculptures created in the workshops, and if all of the baking is done consecutively, the ovens only have to preheat once. Also, if the workshops are held in months with cooler temperatures, the ovens will contribute to heating the sculpture studio to a comfortable temperature, reducing the energy that the studio\u2019s heaters will need to use. She found that the total kilowatt-hours of energy, [latex]y[\/latex], used by the ovens for [latex]x[\/latex] hours of baking time is given by\r\n<p style=\"text-align: center;\">[latex]y=2x+0.5[\/latex]<\/p>\r\nThe equation for the kilowatt-hours of energy, [latex]y[\/latex], that the heaters would use to maintain a comfortable ambient temperature in the studio after [latex]x[\/latex] hours of baking time is perpendicular to the equation above.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31610[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Find the value of a variable that satisfies an equation<\/li>\n<li>Write equations for lines using different forms: slope-intercept, point-slope, and standard form<\/li>\n<li>Recognize and write equations for horizontal and vertical lines<\/li>\n<li>Determine if lines are parallel or perpendicular, and write equations for lines parallel or perpendicular to a given line<\/li>\n<\/ul>\n<\/section>\n<p>The chief financial officer, or CFO, of a company is in charge of financial planning, risk management, budgeting, record keeping, and reporting. Dhakiya is the CFO of a non-profit community arts center.<\/p>\n<p>One of Dhakiya\u2019s responsibilities is to track the sales of fundraising merchandise. She is hoping to raise [latex]$2000[\/latex] in the month of February with sales of merchandise averaging [latex]$75[\/latex] a day. If [latex]y[\/latex] represents the total money raised in [latex]x[\/latex] days of sales, Dhakiya can use a linear equation to model the fundraiser.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm26849\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=26849&theme=lumen&iframe_resize_id=ohm26849&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm26850\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=26850&theme=lumen&iframe_resize_id=ohm26850&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>The fundraising merchandise was created by volunteers using mostly repurposed or donated materials. This way, Dhakiya was able to keep the overhead costs for this fundraiser fairly low. The [latex]y[\/latex]-intercept indicates the overhead cost of materials for the merchandise that will be deducted from the total sales.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm26851\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=26851&theme=lumen&iframe_resize_id=ohm26851&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm26852\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=26852&theme=lumen&iframe_resize_id=ohm26852&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm26853\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=26853&theme=lumen&iframe_resize_id=ohm26853&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Another one of Dhakiya\u2019s responsibilities is applying for grants to fund activities for the youth programs at the community arts center. Dhakiya is applying to two grants that each offer a starting amount and additional funds based on the number of participants in the youth programs. The following equations represent the total funding provided, [latex]y[\/latex], given [latex]x[\/latex] participants in the youth programs.<\/p>\n<ul>\n<li>Grant 1: [latex]y=40(x+25)[\/latex]<\/li>\n<li>Grant 2: [latex]-80x+2y=1600[\/latex]<\/li>\n<\/ul>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31609\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31609&theme=lumen&iframe_resize_id=ohm31609&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<figure id=\"attachment_6725\" aria-describedby=\"caption-attachment-6725\" style=\"width: 200px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6725 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16034058\/blue_clay_3.2-Equations-of-Lines-200x300.jpg\" alt=\"\" width=\"200\" height=\"300\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16034058\/blue_clay_3.2-Equations-of-Lines-200x300.jpg 200w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16034058\/blue_clay_3.2-Equations-of-Lines-682x1024.jpg 682w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16034058\/blue_clay_3.2-Equations-of-Lines-768x1154.jpg 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16034058\/blue_clay_3.2-Equations-of-Lines-1022x1536.jpg 1022w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16034058\/blue_clay_3.2-Equations-of-Lines-65x98.jpg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16034058\/blue_clay_3.2-Equations-of-Lines-225x338.jpg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16034058\/blue_clay_3.2-Equations-of-Lines-350x526.jpg 350w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/16034058\/blue_clay_3.2-Equations-of-Lines.jpg 1065w\" sizes=\"(max-width: 200px) 100vw, 200px\" \/><figcaption id=\"caption-attachment-6725\" class=\"wp-caption-text\">Clay workshop. Photo by Annie Spratt on Unsplash<\/figcaption><\/figure>\n<p>After analyzing the community art center\u2019s energy bills, Dhakiya determined the best plan for the polymer clay workshops that conserves energy. Ovens are used to bake the sculptures created in the workshops, and if all of the baking is done consecutively, the ovens only have to preheat once. Also, if the workshops are held in months with cooler temperatures, the ovens will contribute to heating the sculpture studio to a comfortable temperature, reducing the energy that the studio\u2019s heaters will need to use. She found that the total kilowatt-hours of energy, [latex]y[\/latex], used by the ovens for [latex]x[\/latex] hours of baking time is given by<\/p>\n<p style=\"text-align: center;\">[latex]y=2x+0.5[\/latex]<\/p>\n<p>The equation for the kilowatt-hours of energy, [latex]y[\/latex], that the heaters would use to maintain a comfortable ambient temperature in the studio after [latex]x[\/latex] hours of baking time is perpendicular to the equation above.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31610\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31610&theme=lumen&iframe_resize_id=ohm31610&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":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\/1060"}],"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":20,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1060\/revisions"}],"predecessor-version":[{"id":7972,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1060\/revisions\/7972"}],"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\/1060\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=1060"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1060"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=1060"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=1060"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}