{"id":242,"date":"2023-02-20T17:13:54","date_gmt":"2023-02-20T17:13:54","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/lines-of-best-fit-background-youll-need-3\/"},"modified":"2026-02-27T15:46:43","modified_gmt":"2026-02-27T15:46:43","slug":"module-5-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/module-5-background-youll-need-2\/","title":{"raw":"Module 5: Background You'll Need 4","rendered":"Module 5: Background You&#8217;ll Need 4"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Use a linear function to make predictions.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Modeling a Linear Relationship<\/h2>\r\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\r\n<p>https:\/\/www.youtube.com\/watch?v=-HFFSYcEMCI<\/p>\r\n<\/section>\r\n<p>When Pam first met Kai, he was extremely overweight\u2014almost [latex]100[\/latex] pounds overweight, and for this reason alone, his owner wanted him euthanized. Kai\u2019s life was in danger, and he was miserable, but Pam rescued him. Here are the details of Kai\u2019s journey:<\/p>\r\n<ul>\r\n\t<li><strong>Initial Weight:<\/strong>\u00a0Kai weighed [latex]173[\/latex] pounds before Pam agreed to foster him. She modified his diet and began walking him three times daily.<\/li>\r\n\t<li><strong>Constant Rate of Change:<\/strong>\u00a0A reasonable goal was for Kai to lose about two pounds each week.<\/li>\r\n<\/ul>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1127[\/ohm2_question]<\/section>\r\n<section>\r\n<section class=\"textbox recall\">The familiar slope-intercept form of a linear equation you probably learned about in algebra is [latex]y=mx+b[\/latex], where\r\n\r\n\r\n<ul>\r\n\t<li>[latex]x[\/latex] represents the <strong>explanatory (independent) variable<\/strong> represented on the horizontal axis.<\/li>\r\n\t<li>[latex]y[\/latex] represents the <strong>response (dependent) variable<\/strong> represented on the vertical axis.<\/li>\r\n\t<li>[latex]m[\/latex] represents the constant rate of change (the slope), and<\/li>\r\n\t<li>[latex]b[\/latex] represents the initial value in a given scenario (which can be zero or negative).<\/li>\r\n<\/ul>\r\n<\/section>\r\n<\/section>\r\n<section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1136[\/ohm2_question]<\/section>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1129[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Use a linear function to make predictions.<\/li>\n<\/ul>\n<\/section>\n<h2>Modeling a Linear Relationship<\/h2>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"173-Pound Golden Retriever Loses Over 100 Pounds | The Dodo\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/-HFFSYcEMCI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/section>\n<p>When Pam first met Kai, he was extremely overweight\u2014almost [latex]100[\/latex] pounds overweight, and for this reason alone, his owner wanted him euthanized. Kai\u2019s life was in danger, and he was miserable, but Pam rescued him. Here are the details of Kai\u2019s journey:<\/p>\n<ul>\n<li><strong>Initial Weight:<\/strong>\u00a0Kai weighed [latex]173[\/latex] pounds before Pam agreed to foster him. She modified his diet and began walking him three times daily.<\/li>\n<li><strong>Constant Rate of Change:<\/strong>\u00a0A reasonable goal was for Kai to lose about two pounds each week.<\/li>\n<\/ul>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1127\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1127&theme=lumen&iframe_resize_id=ohm1127&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>\n<section class=\"textbox recall\">The familiar slope-intercept form of a linear equation you probably learned about in algebra is [latex]y=mx+b[\/latex], where<\/p>\n<ul>\n<li>[latex]x[\/latex] represents the <strong>explanatory (independent) variable<\/strong> represented on the horizontal axis.<\/li>\n<li>[latex]y[\/latex] represents the <strong>response (dependent) variable<\/strong> represented on the vertical axis.<\/li>\n<li>[latex]m[\/latex] represents the constant rate of change (the slope), and<\/li>\n<li>[latex]b[\/latex] represents the initial value in a given scenario (which can be zero or negative).<\/li>\n<\/ul>\n<\/section>\n<\/section>\n<section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1136\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1136&theme=lumen&iframe_resize_id=ohm1136&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1129\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1129&theme=lumen&iframe_resize_id=ohm1129&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":12,"menu_order":5,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":225,"module-header":"background_you_need","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\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/242"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":17,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/242\/revisions"}],"predecessor-version":[{"id":7136,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/242\/revisions\/7136"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/225"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/242\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=242"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=242"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=242"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=242"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}