{"id":2829,"date":"2025-08-13T18:48:00","date_gmt":"2025-08-13T18:48:00","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=2829"},"modified":"2026-01-31T02:14:17","modified_gmt":"2026-01-31T02:14:17","slug":"introduction-to-calculus-background-youll-need-4","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/introduction-to-calculus-background-youll-need-4\/","title":{"raw":"Introduction to Calculus: Background You'll Need 4","rendered":"Introduction to Calculus: Background You&#8217;ll Need 4"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Write linear equations using point-slope form<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2 id=\"Introduction\" class=\"no-indent\" style=\"text-align: left;\">Point-Slope Form of a Linear Equation<\/h2>\r\nA linear equation represents a straight line. When the slope of a line and a point on the line are known, the equation can be written using <strong>point-slope form<\/strong>.\r\n\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>Point-slope form<\/h3>\r\nThe point-slope form of a linear equation is\r\n[latex]y - y_1 = m(x - x_1)[\/latex],\r\nwhere [latex]m[\/latex] is the slope and ([latex]x_1, y_1[\/latex]) is a point on the line.\r\n\r\n<\/div>\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">Write the equation of the line with a slope, [latex]m=3[\/latex], that passes through the point [latex](2,-4)[\/latex].\r\n\r\n[reveal-answer q=\"941635\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"941635\"]\r\n\r\nThe given point is [latex](x_1,y_1)[\/latex].\r\n\r\nSubstitute the values into the point-slope formula:\r\n\r\n[latex]y - y_1 = m(x - x_1)[\/latex]\r\n\r\n[latex]y - (-4) = 3(x - 2)[\/latex]\r\n\r\n[latex]y+4=3(x-2)[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\">[ohm_question hide_question_numbers=1]319417[\/ohm_question]<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Write linear equations using point-slope form<\/li>\n<\/ul>\n<\/section>\n<h2 id=\"Introduction\" class=\"no-indent\" style=\"text-align: left;\">Point-Slope Form of a Linear Equation<\/h2>\n<p>A linear equation represents a straight line. When the slope of a line and a point on the line are known, the equation can be written using <strong>point-slope form<\/strong>.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>Point-slope form<\/h3>\n<p>The point-slope form of a linear equation is<br \/>\n[latex]y - y_1 = m(x - x_1)[\/latex],<br \/>\nwhere [latex]m[\/latex] is the slope and ([latex]x_1, y_1[\/latex]) is a point on the line.<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">Write the equation of the line with a slope, [latex]m=3[\/latex], that passes through the point [latex](2,-4)[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q941635\">Show Solution<\/button><\/p>\n<div id=\"q941635\" class=\"hidden-answer\" style=\"display: none\">\n<p>The given point is [latex](x_1,y_1)[\/latex].<\/p>\n<p>Substitute the values into the point-slope formula:<\/p>\n<p>[latex]y - y_1 = m(x - x_1)[\/latex]<\/p>\n<p>[latex]y - (-4) = 3(x - 2)[\/latex]<\/p>\n<p>[latex]y+4=3(x-2)[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm319417\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=319417&theme=lumen&iframe_resize_id=ohm319417&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":67,"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":263,"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\/2829"}],"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":4,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2829\/revisions"}],"predecessor-version":[{"id":5482,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2829\/revisions\/5482"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/263"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2829\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=2829"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=2829"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=2829"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=2829"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}