{"id":2647,"date":"2025-08-13T18:21:08","date_gmt":"2025-08-13T18:21:08","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=2647"},"modified":"2025-09-16T19:38:29","modified_gmt":"2025-09-16T19:38:29","slug":"systems-of-equations-and-inequalities-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/systems-of-equations-and-inequalities-background-youll-need-2\/","title":{"raw":"Systems of Equations and Inequalities: Background You'll Need 2","rendered":"Systems of Equations and Inequalities: Background You&#8217;ll Need 2"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li><span data-sheets-root=\"1\">Graph linear functions<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p data-start=\"2194\" data-end=\"2333\">A linear function looks like [latex]y=mx+b[\/latex], where [latex]m[\/latex] is slope and [latex]b[\/latex] is the [latex]y[\/latex]-intercept.<\/p>\r\n\r\n<section class=\"textbox example\" aria-label=\"Example\">Graph [latex]y=-\\tfrac{2}{3}x+4[\/latex].\r\n<ul>\r\n \t<li>Intercept: [latex](0,4)[\/latex]<\/li>\r\n \t<li>Slope: [latex]-\\frac{2}{3}[\/latex] translates to\r\n<ul>\r\n \t<li>Down 2 units<\/li>\r\n \t<li>Right 3 units<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\nStep 1: Graph the intercept\r\n\r\n<img class=\"alignnone  wp-image-4036\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181132\/Screenshot-2025-09-16-at-11.11.21%E2%80%AFAM.png\" alt=\"\" width=\"237\" height=\"240\" \/>\r\n\r\nStep 2: Use the slope to find a second point\r\n\r\n<img class=\"alignnone  wp-image-4037\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181224\/Screenshot-2025-09-16-at-11.12.14%E2%80%AFAM.png\" alt=\"\" width=\"244\" height=\"216\" \/>\r\n\r\nStep 3: Draw the line through the points\r\n\r\n<img class=\"alignnone  wp-image-4038\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181444\/Screenshot-2025-09-16-at-11.14.34%E2%80%AFAM.png\" alt=\"\" width=\"243\" height=\"243\" \/>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]312216[\/ohm_question]\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li><span data-sheets-root=\"1\">Graph linear functions<\/span><\/li>\n<\/ul>\n<\/section>\n<p data-start=\"2194\" data-end=\"2333\">A linear function looks like [latex]y=mx+b[\/latex], where [latex]m[\/latex] is slope and [latex]b[\/latex] is the [latex]y[\/latex]-intercept.<\/p>\n<section class=\"textbox example\" aria-label=\"Example\">Graph [latex]y=-\\tfrac{2}{3}x+4[\/latex].<\/p>\n<ul>\n<li>Intercept: [latex](0,4)[\/latex]<\/li>\n<li>Slope: [latex]-\\frac{2}{3}[\/latex] translates to\n<ul>\n<li>Down 2 units<\/li>\n<li>Right 3 units<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>Step 1: Graph the intercept<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone  wp-image-4036\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181132\/Screenshot-2025-09-16-at-11.11.21%E2%80%AFAM.png\" alt=\"\" width=\"237\" height=\"240\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181132\/Screenshot-2025-09-16-at-11.11.21%E2%80%AFAM.png 1058w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181132\/Screenshot-2025-09-16-at-11.11.21%E2%80%AFAM-296x300.png 296w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181132\/Screenshot-2025-09-16-at-11.11.21%E2%80%AFAM-1011x1024.png 1011w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181132\/Screenshot-2025-09-16-at-11.11.21%E2%80%AFAM-768x778.png 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181132\/Screenshot-2025-09-16-at-11.11.21%E2%80%AFAM-65x66.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181132\/Screenshot-2025-09-16-at-11.11.21%E2%80%AFAM-225x228.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181132\/Screenshot-2025-09-16-at-11.11.21%E2%80%AFAM-350x355.png 350w\" sizes=\"(max-width: 237px) 100vw, 237px\" \/><\/p>\n<p>Step 2: Use the slope to find a second point<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone  wp-image-4037\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181224\/Screenshot-2025-09-16-at-11.12.14%E2%80%AFAM.png\" alt=\"\" width=\"244\" height=\"216\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181224\/Screenshot-2025-09-16-at-11.12.14%E2%80%AFAM.png 956w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181224\/Screenshot-2025-09-16-at-11.12.14%E2%80%AFAM-300x265.png 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181224\/Screenshot-2025-09-16-at-11.12.14%E2%80%AFAM-768x680.png 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181224\/Screenshot-2025-09-16-at-11.12.14%E2%80%AFAM-65x58.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181224\/Screenshot-2025-09-16-at-11.12.14%E2%80%AFAM-225x199.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181224\/Screenshot-2025-09-16-at-11.12.14%E2%80%AFAM-350x310.png 350w\" sizes=\"(max-width: 244px) 100vw, 244px\" \/><\/p>\n<p>Step 3: Draw the line through the points<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone  wp-image-4038\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181444\/Screenshot-2025-09-16-at-11.14.34%E2%80%AFAM.png\" alt=\"\" width=\"243\" height=\"243\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181444\/Screenshot-2025-09-16-at-11.14.34%E2%80%AFAM.png 1058w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181444\/Screenshot-2025-09-16-at-11.14.34%E2%80%AFAM-300x300.png 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181444\/Screenshot-2025-09-16-at-11.14.34%E2%80%AFAM-1024x1024.png 1024w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181444\/Screenshot-2025-09-16-at-11.14.34%E2%80%AFAM-150x150.png 150w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181444\/Screenshot-2025-09-16-at-11.14.34%E2%80%AFAM-768x768.png 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181444\/Screenshot-2025-09-16-at-11.14.34%E2%80%AFAM-65x65.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181444\/Screenshot-2025-09-16-at-11.14.34%E2%80%AFAM-225x225.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/16181444\/Screenshot-2025-09-16-at-11.14.34%E2%80%AFAM-350x350.png 350w\" sizes=\"(max-width: 243px) 100vw, 243px\" \/><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm312216\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=312216&theme=lumen&iframe_resize_id=ohm312216&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":67,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":131,"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\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2647"}],"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\/67"}],"version-history":[{"count":3,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2647\/revisions"}],"predecessor-version":[{"id":4039,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2647\/revisions\/4039"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/131"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2647\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=2647"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=2647"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=2647"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=2647"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}