{"id":8134,"date":"2023-09-20T17:49:12","date_gmt":"2023-09-20T17:49:12","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=8134"},"modified":"2025-08-28T04:29:17","modified_gmt":"2025-08-28T04:29:17","slug":"linear-functions-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/linear-functions-apply-it-1\/","title":{"raw":"Linear Functions: Apply It 1","rendered":"Linear Functions: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Express a linear function using an equation, words, tables, and graphs<\/li>\r\n\t<li>Determine whether a linear function is increasing, decreasing, or constant.<\/li>\r\n\t<li>Calculate and interpret slope<\/li>\r\n\t<li>Find the x-intercept of a linear function given its equation<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2><strong>Linear Landscapes: Exploring Slopes and Intercepts<\/strong><\/h2>\r\n<p>Jada, an urban planner, is designing a new park in the city. The park's pathways are represented by linear functions on her map. She needs to calculate various aspects of these pathways to ensure they meet the city's design standards.<\/p>\r\n<center>\r\n[caption id=\"attachment_10443\" align=\"aligncenter\" width=\"500\"]<img class=\"wp-image-10443\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/07184121\/2012__Little_Stoke_Park_Recreational_Ground_-_geograph.org_.uk_-_2810689.jpg\" alt=\"A grassy park\" width=\"500\" height=\"353\" \/> Figure 1. Help Jada calculate the pathways for the city park[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>Jada shows you the blueprint of a pathway represented by the equation [latex]y=2x-5[\/latex] . She asks you to graph this function and determine its key features.<\/p>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]13869[\/ohm2_question]<\/p>\r\n<\/section>\r\n<p>The slope and [latex]y[\/latex]-intercept of the graph can tell more than just the direction and starting point of the path. They also give insight into how accessible the path will be for visitors. Jada needs to ensure the pathway is accessible, which means it cannot be too steep.<\/p>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]13870[\/ohm2_question]<\/p>\r\n<\/section>\r\n<p>Understanding the slope's impact on accessibility, Jada now wants to communicate these changes to the city council in a clear and concise manner. A table would be the perfect way to visualize the elevation changes over the distance of the pathway.<\/p>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]13871[\/ohm2_question]<\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Express a linear function using an equation, words, tables, and graphs<\/li>\n<li>Determine whether a linear function is increasing, decreasing, or constant.<\/li>\n<li>Calculate and interpret slope<\/li>\n<li>Find the x-intercept of a linear function given its equation<\/li>\n<\/ul>\n<\/section>\n<h2><strong>Linear Landscapes: Exploring Slopes and Intercepts<\/strong><\/h2>\n<p>Jada, an urban planner, is designing a new park in the city. The park&#8217;s pathways are represented by linear functions on her map. She needs to calculate various aspects of these pathways to ensure they meet the city&#8217;s design standards.<\/p>\n<div style=\"text-align: center;\">\n<figure id=\"attachment_10443\" aria-describedby=\"caption-attachment-10443\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-10443\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/07184121\/2012__Little_Stoke_Park_Recreational_Ground_-_geograph.org_.uk_-_2810689.jpg\" alt=\"A grassy park\" width=\"500\" height=\"353\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/07184121\/2012__Little_Stoke_Park_Recreational_Ground_-_geograph.org_.uk_-_2810689.jpg 640w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/07184121\/2012__Little_Stoke_Park_Recreational_Ground_-_geograph.org_.uk_-_2810689-300x212.jpg 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/07184121\/2012__Little_Stoke_Park_Recreational_Ground_-_geograph.org_.uk_-_2810689-65x46.jpg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/07184121\/2012__Little_Stoke_Park_Recreational_Ground_-_geograph.org_.uk_-_2810689-225x159.jpg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/09\/07184121\/2012__Little_Stoke_Park_Recreational_Ground_-_geograph.org_.uk_-_2810689-350x247.jpg 350w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-10443\" class=\"wp-caption-text\">Figure 1. Help Jada calculate the pathways for the city park<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Jada shows you the blueprint of a pathway represented by the equation [latex]y=2x-5[\/latex] . She asks you to graph this function and determine its key features.<\/p>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm13869\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13869&theme=lumen&iframe_resize_id=ohm13869&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<p>The slope and [latex]y[\/latex]-intercept of the graph can tell more than just the direction and starting point of the path. They also give insight into how accessible the path will be for visitors. Jada needs to ensure the pathway is accessible, which means it cannot be too steep.<\/p>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm13870\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13870&theme=lumen&iframe_resize_id=ohm13870&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<p>Understanding the slope&#8217;s impact on accessibility, Jada now wants to communicate these changes to the city council in a clear and concise manner. A table would be the perfect way to visualize the elevation changes over the distance of the pathway.<\/p>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm13871\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13871&theme=lumen&iframe_resize_id=ohm13871&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n","protected":false},"author":15,"menu_order":18,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"2012 : Little Stoke Park Recreational Ground\",\"author\":\"Maurice Pullin\",\"organization\":\"Wiki Commons\",\"url\":\"https:\/\/commons.wikimedia.org\/w\/index.php?search=park+&title=Special:MediaSearch&go=Go&type=image\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":72,"module-header":"apply_it","content_attributions":[{"type":"cc-attribution","description":"2012 : Little Stoke Park Recreational Ground","author":"Maurice Pullin","organization":"Wiki Commons","url":"https:\/\/commons.wikimedia.org\/w\/index.php?search=park+&title=Special:MediaSearch&go=Go&type=image","project":"","license":"cc-by-sa","license_terms":""}],"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\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8134"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":15,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8134\/revisions"}],"predecessor-version":[{"id":15835,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8134\/revisions\/15835"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/72"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8134\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=8134"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=8134"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=8134"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=8134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}