{"id":778,"date":"2025-07-15T16:08:58","date_gmt":"2025-07-15T16:08:58","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=778"},"modified":"2025-12-30T16:50:14","modified_gmt":"2025-12-30T16:50:14","slug":"linear-functions-learn-it-7","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/linear-functions-learn-it-7\/","title":{"raw":"Linear Functions: Learn It 7","rendered":"Linear Functions: Learn It 7"},"content":{"raw":"<h2 data-start=\"411\" data-end=\"500\">Writing Equations of Parallel and Perpendicular Lines to Horizontal and Vertical Lines<\/h2>\r\n<section class=\"textbox recall\" aria-label=\"Recall\">\r\n<ul>\r\n \t<li>\r\n<p data-start=\"502\" data-end=\"655\">A <strong data-start=\"504\" data-end=\"523\">horizontal line<\/strong> has the form [latex]y = c[\/latex]<\/p>\r\n<\/li>\r\n \t<li>\r\n<p data-start=\"502\" data-end=\"655\"><span style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\">A <\/span><strong style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\" data-start=\"659\" data-end=\"676\">vertical line<\/strong><span style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\"> has the form <\/span><span style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\">[latex]x = c[\/latex]<\/span><\/p>\r\n<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h3>Parallel to Horizontal or Vertical Lines<\/h3>\r\n<section class=\"textbox example\">(a) Write the equation of a line parallel to [latex]y = 4[\/latex] that goes through the point [latex](\u20133, 2)[\/latex].\r\n\r\n[reveal-answer q=\"282508\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"282508\"] A line parallel to [latex]y = 4[\/latex] is also horizontal. It will have the same [latex]y[\/latex]-value at all points. So, the equation is: [latex]y = 2[\/latex][\/hidden-answer]\r\n\r\n(b) Write the equation of a line parallel to [latex]x = \u20135[\/latex] that passes through the point [latex](2, 1)[\/latex].\r\n\r\n\r\n[reveal-answer q=\"56963\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"56963\"]A line parallel to [latex]x = \u20135[\/latex] is another vertical line. It must pass through [latex]x = 2[\/latex], so the equation is: [latex]x = 2[\/latex][\/hidden-answer]<\/section>\r\n<h3 data-start=\"1834\" data-end=\"1857\">Perpendicular to Horizontal or Vertical Lines<\/h3>\r\n<section class=\"textbox example\">(a) Write the equation of a line perpendicular to [latex]y = 4[\/latex] that passes through the point [latex](\u20131, 4)[\/latex].Since [latex]y = 4[\/latex] is a horizontal line, the perpendicular line must be vertical.\r\nIt passes through [latex]x = \u20131[\/latex], so the equation is:\r\n[latex]x = \u20131[\/latex](b) Write the equation of a line perpendicular to [latex]x = \u20132[\/latex] that passes through the point [latex](\u20132, 3)[\/latex].Since [latex]x = \u20132[\/latex] is vertical, the perpendicular line must be horizontal.\r\nIt passes through [latex]y = 3[\/latex], so the equation is:\r\n[latex]y = 3[\/latex]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]314647[\/ohm_question]<\/section><section class=\"textbox questionHelp\" aria-label=\"Question Help\">\r\n<p data-start=\"2859\" data-end=\"2949\"><strong data-start=\"2859\" data-end=\"2949\">Writing equations of lines parallel or perpendicular to horizontal and vertical lines:<\/strong><\/p>\r\n\r\n<ul data-start=\"2951\" data-end=\"3332\">\r\n \t<li data-start=\"2951\" data-end=\"3047\">\r\n<p data-start=\"2953\" data-end=\"3047\">A line <strong data-start=\"2960\" data-end=\"2996\">parallel to [latex]y = c[\/latex]<\/strong> is another horizontal line: [latex]y = d[\/latex]<\/p>\r\n<\/li>\r\n \t<li data-start=\"3048\" data-end=\"3142\">\r\n<p data-start=\"3050\" data-end=\"3142\">A line <strong data-start=\"3057\" data-end=\"3093\">parallel to [latex]x = c[\/latex]<\/strong> is another vertical line: [latex]x = d[\/latex]<\/p>\r\n<\/li>\r\n \t<li data-start=\"3143\" data-end=\"3236\">\r\n<p data-start=\"3145\" data-end=\"3236\">A line <strong data-start=\"3152\" data-end=\"3193\">perpendicular to [latex]y = c[\/latex]<\/strong> is a vertical line: [latex]x = d[\/latex]<\/p>\r\n<\/li>\r\n \t<li data-start=\"3237\" data-end=\"3332\">\r\n<p data-start=\"3239\" data-end=\"3332\">A line <strong data-start=\"3246\" data-end=\"3287\">perpendicular to [latex]x = c[\/latex]<\/strong> is a horizontal line: [latex]y = d[\/latex]<\/p>\r\n<\/li>\r\n<\/ul>\r\n<p data-start=\"3334\" data-end=\"3412\">Use the point given to find the value of [latex]x[\/latex] or [latex]y[\/latex].<\/p>\r\n\r\n<\/section>","rendered":"<h2 data-start=\"411\" data-end=\"500\">Writing Equations of Parallel and Perpendicular Lines to Horizontal and Vertical Lines<\/h2>\n<section class=\"textbox recall\" aria-label=\"Recall\">\n<ul>\n<li>\n<p data-start=\"502\" data-end=\"655\">A <strong data-start=\"504\" data-end=\"523\">horizontal line<\/strong> has the form [latex]y = c[\/latex]<\/p>\n<\/li>\n<li>\n<p data-start=\"502\" data-end=\"655\"><span style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\">A <\/span><strong style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\" data-start=\"659\" data-end=\"676\">vertical line<\/strong><span style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\"> has the form <\/span><span style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\">[latex]x = c[\/latex]<\/span><\/p>\n<\/li>\n<\/ul>\n<\/section>\n<h3>Parallel to Horizontal or Vertical Lines<\/h3>\n<section class=\"textbox example\">(a) Write the equation of a line parallel to [latex]y = 4[\/latex] that goes through the point [latex](\u20133, 2)[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q282508\">Show Solution<\/button><\/p>\n<div id=\"q282508\" class=\"hidden-answer\" style=\"display: none\"> A line parallel to [latex]y = 4[\/latex] is also horizontal. It will have the same [latex]y[\/latex]-value at all points. So, the equation is: [latex]y = 2[\/latex]<\/div>\n<\/div>\n<p>(b) Write the equation of a line parallel to [latex]x = \u20135[\/latex] that passes through the point [latex](2, 1)[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q56963\">Show Solution<\/button><\/p>\n<div id=\"q56963\" class=\"hidden-answer\" style=\"display: none\">A line parallel to [latex]x = \u20135[\/latex] is another vertical line. It must pass through [latex]x = 2[\/latex], so the equation is: [latex]x = 2[\/latex]<\/div>\n<\/div>\n<\/section>\n<h3 data-start=\"1834\" data-end=\"1857\">Perpendicular to Horizontal or Vertical Lines<\/h3>\n<section class=\"textbox example\">(a) Write the equation of a line perpendicular to [latex]y = 4[\/latex] that passes through the point [latex](\u20131, 4)[\/latex].Since [latex]y = 4[\/latex] is a horizontal line, the perpendicular line must be vertical.<br \/>\nIt passes through [latex]x = \u20131[\/latex], so the equation is:<br \/>\n[latex]x = \u20131[\/latex](b) Write the equation of a line perpendicular to [latex]x = \u20132[\/latex] that passes through the point [latex](\u20132, 3)[\/latex].Since [latex]x = \u20132[\/latex] is vertical, the perpendicular line must be horizontal.<br \/>\nIt passes through [latex]y = 3[\/latex], so the equation is:<br \/>\n[latex]y = 3[\/latex]<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm314647\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=314647&theme=lumen&iframe_resize_id=ohm314647&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\">\n<p data-start=\"2859\" data-end=\"2949\"><strong data-start=\"2859\" data-end=\"2949\">Writing equations of lines parallel or perpendicular to horizontal and vertical lines:<\/strong><\/p>\n<ul data-start=\"2951\" data-end=\"3332\">\n<li data-start=\"2951\" data-end=\"3047\">\n<p data-start=\"2953\" data-end=\"3047\">A line <strong data-start=\"2960\" data-end=\"2996\">parallel to [latex]y = c[\/latex]<\/strong> is another horizontal line: [latex]y = d[\/latex]<\/p>\n<\/li>\n<li data-start=\"3048\" data-end=\"3142\">\n<p data-start=\"3050\" data-end=\"3142\">A line <strong data-start=\"3057\" data-end=\"3093\">parallel to [latex]x = c[\/latex]<\/strong> is another vertical line: [latex]x = d[\/latex]<\/p>\n<\/li>\n<li data-start=\"3143\" data-end=\"3236\">\n<p data-start=\"3145\" data-end=\"3236\">A line <strong data-start=\"3152\" data-end=\"3193\">perpendicular to [latex]y = c[\/latex]<\/strong> is a vertical line: [latex]x = d[\/latex]<\/p>\n<\/li>\n<li data-start=\"3237\" data-end=\"3332\">\n<p data-start=\"3239\" data-end=\"3332\">A line <strong data-start=\"3246\" data-end=\"3287\">perpendicular to [latex]x = c[\/latex]<\/strong> is a horizontal line: [latex]y = d[\/latex]<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"3334\" data-end=\"3412\">Use the point given to find the value of [latex]x[\/latex] or [latex]y[\/latex].<\/p>\n<\/section>\n","protected":false},"author":13,"menu_order":20,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":61,"module-header":"learn_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\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/778"}],"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\/13"}],"version-history":[{"count":7,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/778\/revisions"}],"predecessor-version":[{"id":5153,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/778\/revisions\/5153"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/61"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/778\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=778"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=778"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=778"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=778"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}