{"id":15977,"date":"2025-06-10T21:47:17","date_gmt":"2025-06-10T21:47:17","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=15977"},"modified":"2025-06-10T21:47:18","modified_gmt":"2025-06-10T21:47:18","slug":"which-of-the-following-is-an-equation-of-a-line-with-slope-5-and-y-intercept-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-of-the-following-is-an-equation-of-a-line-with-slope-5-and-y-intercept-2\/","title":{"rendered":"Which of the following is an equation of a line with slope 5 and y-intercept 2"},"content":{"rendered":"\n<p>Which of the following is an equation of a line with slope 5 and y-intercept 2?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p>To find the equation of a line with a <strong>slope of 5<\/strong> and a <strong>y-intercept of 2<\/strong>, we use the <strong>slope-intercept form<\/strong> of a linear equation: y=mx+by = mx + b<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>mm is the <strong>slope<\/strong> of the line<\/li>\n\n\n\n<li>bb is the <strong>y-intercept<\/strong>, which is the value of yy when x=0x = 0<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Given:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Slope m=5m = 5<\/li>\n\n\n\n<li>Y-intercept b=2b = 2<\/li>\n<\/ul>\n\n\n\n<p>Substitute these values into the slope-intercept form: y=5x+2y = 5x + 2<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Correct Answer:<\/strong><\/h3>\n\n\n\n<p>y=5x+2y = 5x + 2<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u270d\ufe0f Explanation (300 words):<\/h3>\n\n\n\n<p>In algebra, the equation of a straight line can be written in several forms, but the most common and easiest to interpret is the <strong>slope-intercept form<\/strong>, which is written as: y=mx+by = mx + b<\/p>\n\n\n\n<p>This form is helpful because it gives us two key pieces of information immediately:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The <strong>slope<\/strong> of the line, mm, which tells us how steep the line is or how much yy increases (or decreases) as xx increases by 1.<\/li>\n\n\n\n<li>The <strong>y-intercept<\/strong>, bb, which is the point where the line crosses the y-axis (i.e., where x=0x = 0).<\/li>\n<\/ol>\n\n\n\n<p>In the problem, we are told that the slope of the line is 5. This means for every increase of 1 in xx, the value of yy increases by 5. Also, the y-intercept is 2, so the line crosses the y-axis at the point (0, 2).<\/p>\n\n\n\n<p>Substituting these values into the slope-intercept form gives: y=5x+2y = 5x + 2<\/p>\n\n\n\n<p>This equation means the line rises quickly due to its steep slope of 5 and starts at the y-axis at 2. It&#8217;s a linear relationship between xx and yy, showing that for every unit increase in xx, yy increases by 5 units from the base of 2.<\/p>\n\n\n\n<p>Understanding this form is foundational for solving graphing problems, analyzing data, and modeling real-world relationships in algebra.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which of the following is an equation of a line with slope 5 and y-intercept 2? The correct answer and explanation is: To find the equation of a line with a slope of 5 and a y-intercept of 2, we use the slope-intercept form of a linear equation: y=mx+by = mx + b Where: Given: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-15977","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/15977","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=15977"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/15977\/revisions"}],"predecessor-version":[{"id":15978,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/15977\/revisions\/15978"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=15977"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=15977"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=15977"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}