{"id":2618,"date":"2025-08-13T18:15:35","date_gmt":"2025-08-13T18:15:35","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=2618"},"modified":"2026-02-24T21:24:18","modified_gmt":"2026-02-24T21:24:18","slug":"exponential-and-logarithmic-functions-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/exponential-and-logarithmic-functions-background-youll-need-2\/","title":{"raw":"Exponential and Logarithmic Functions: Background You'll Need 2","rendered":"Exponential and Logarithmic Functions: Background You&#8217;ll Need 2"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Write the equation of horizontal and vertical lines given their graphs<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2 data-start=\"211\" data-end=\"265\">Writing Equations of Horizontal and Vertical Lines<\/h2>\r\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\r\n<div>\r\n<h3>horizontal and vertical lines<\/h3>\r\n<ul>\r\n \t<li>A <strong data-start=\"538\" data-end=\"557\">horizontal line<\/strong> has the equation [latex]y=c[\/latex] and is flat, running left to right across the coordinate plane.<\/li>\r\n \t<li>A <strong data-start=\"1095\" data-end=\"1112\">vertical line<\/strong> has the equation [latex]x=c[\/latex] and goes straight up and down on the coordinate plane.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">\r\n<p data-start=\"840\" data-end=\"896\">Write the equation of the line shown.<\/p>\r\n<p data-start=\"840\" data-end=\"896\"><img class=\"alignnone wp-image-3863\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/11171211\/Screenshot-2025-09-11-at-10.11.58%E2%80%AFAM.png\" alt=\"Horizontal line on coordinate plane through the y-axis at 3.\" width=\"223\" height=\"217\" \/><\/p>\r\n<p data-start=\"840\" data-end=\"896\">[reveal-answer q=\"856243\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"856243\"]<\/p>\r\n<p data-start=\"840\" data-end=\"896\">Looking at the graph, the line passes through [latex](0,3)[\/latex], [latex](2,3)[\/latex], and [latex](-4,3)[\/latex]. In every case, [latex]y=3[\/latex].<\/p>\r\n<p data-start=\"840\" data-end=\"896\">Therefore, the equation is: [latex]y=3[\/latex][\/hidden-answer]<\/p>\r\n\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">\r\n<p data-start=\"1385\" data-end=\"1441\">Write the equation of the line shown.<\/p>\r\n<p data-start=\"1385\" data-end=\"1441\"><img class=\"alignnone wp-image-3864\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/11171356\/Screenshot-2025-09-11-at-10.13.35%E2%80%AFAM.png\" alt=\"Vertical line on coordinate plane through the x-axis at negative 2.\" width=\"221\" height=\"215\" \/><\/p>\r\n<p data-start=\"1385\" data-end=\"1441\">[reveal-answer q=\"681312\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"681312\"]<\/p>\r\n<p data-start=\"1445\" data-end=\"1536\">Looking at the graph, the line passes through [latex](-2,0)[\/latex], [latex](-2,4)[\/latex], and [latex](-2,-5)[\/latex]. In every case, [latex]x=-2[\/latex].<\/p>\r\n<p data-start=\"1445\" data-end=\"1536\">Therefore, the equation is: [latex]x=-2[\/latex].<\/p>\r\n<p data-start=\"1385\" data-end=\"1441\">[\/hidden-answer]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]311406[\/ohm_question]<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Write the equation of horizontal and vertical lines given their graphs<\/li>\n<\/ul>\n<\/section>\n<h2 data-start=\"211\" data-end=\"265\">Writing Equations of Horizontal and Vertical Lines<\/h2>\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\n<div>\n<h3>horizontal and vertical lines<\/h3>\n<ul>\n<li>A <strong data-start=\"538\" data-end=\"557\">horizontal line<\/strong> has the equation [latex]y=c[\/latex] and is flat, running left to right across the coordinate plane.<\/li>\n<li>A <strong data-start=\"1095\" data-end=\"1112\">vertical line<\/strong> has the equation [latex]x=c[\/latex] and goes straight up and down on the coordinate plane.<\/li>\n<\/ul>\n<\/div>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p data-start=\"840\" data-end=\"896\">Write the equation of the line shown.<\/p>\n<p data-start=\"840\" data-end=\"896\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3863\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/11171211\/Screenshot-2025-09-11-at-10.11.58%E2%80%AFAM.png\" alt=\"Horizontal line on coordinate plane through the y-axis at 3.\" width=\"223\" height=\"217\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/11171211\/Screenshot-2025-09-11-at-10.11.58%E2%80%AFAM.png 548w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/11171211\/Screenshot-2025-09-11-at-10.11.58%E2%80%AFAM-300x291.png 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/11171211\/Screenshot-2025-09-11-at-10.11.58%E2%80%AFAM-65x63.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/11171211\/Screenshot-2025-09-11-at-10.11.58%E2%80%AFAM-225x218.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/11171211\/Screenshot-2025-09-11-at-10.11.58%E2%80%AFAM-350x340.png 350w\" sizes=\"(max-width: 223px) 100vw, 223px\" \/><\/p>\n<p data-start=\"840\" data-end=\"896\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q856243\">Show Solution<\/button><\/p>\n<div id=\"q856243\" class=\"hidden-answer\" style=\"display: none\">\n<p data-start=\"840\" data-end=\"896\">Looking at the graph, the line passes through [latex](0,3)[\/latex], [latex](2,3)[\/latex], and [latex](-4,3)[\/latex]. In every case, [latex]y=3[\/latex].<\/p>\n<p data-start=\"840\" data-end=\"896\">Therefore, the equation is: [latex]y=3[\/latex]<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p data-start=\"1385\" data-end=\"1441\">Write the equation of the line shown.<\/p>\n<p data-start=\"1385\" data-end=\"1441\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3864\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/11171356\/Screenshot-2025-09-11-at-10.13.35%E2%80%AFAM.png\" alt=\"Vertical line on coordinate plane through the x-axis at negative 2.\" width=\"221\" height=\"215\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/11171356\/Screenshot-2025-09-11-at-10.13.35%E2%80%AFAM.png 538w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/11171356\/Screenshot-2025-09-11-at-10.13.35%E2%80%AFAM-300x292.png 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/11171356\/Screenshot-2025-09-11-at-10.13.35%E2%80%AFAM-65x63.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/11171356\/Screenshot-2025-09-11-at-10.13.35%E2%80%AFAM-225x219.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/11171356\/Screenshot-2025-09-11-at-10.13.35%E2%80%AFAM-350x341.png 350w\" sizes=\"(max-width: 221px) 100vw, 221px\" \/><\/p>\n<p data-start=\"1385\" data-end=\"1441\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q681312\">Show Solution<\/button><\/p>\n<div id=\"q681312\" class=\"hidden-answer\" style=\"display: none\">\n<p data-start=\"1445\" data-end=\"1536\">Looking at the graph, the line passes through [latex](-2,0)[\/latex], [latex](-2,4)[\/latex], and [latex](-2,-5)[\/latex]. In every case, [latex]x=-2[\/latex].<\/p>\n<p data-start=\"1445\" data-end=\"1536\">Therefore, the equation is: [latex]x=-2[\/latex].<\/p>\n<p data-start=\"1385\" data-end=\"1441\"><\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm311406\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=311406&theme=lumen&iframe_resize_id=ohm311406&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/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":105,"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\/2618"}],"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":6,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2618\/revisions"}],"predecessor-version":[{"id":5728,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2618\/revisions\/5728"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/105"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2618\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=2618"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=2618"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=2618"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=2618"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}