{"id":40189,"date":"2025-06-27T14:23:49","date_gmt":"2025-06-27T14:23:49","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=40189"},"modified":"2025-06-27T14:23:50","modified_gmt":"2025-06-27T14:23:50","slug":"a-graph-has-the-equation-x-2y-4-0","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-graph-has-the-equation-x-2y-4-0\/","title":{"rendered":"A graph has the equation x + 2y + 4 = 0"},"content":{"rendered":"\n<p>A graph has the equation x + 2y + 4 = 0. a) Show that this is the equation of a straight line. b) Find the gradient of the line. c) Draw a graph of the line.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">a) Show that this is the equation of a straight line<\/h3>\n\n\n\n<p>The given equation is:<br><strong>x + 2y + 4 = 0<\/strong><\/p>\n\n\n\n<p>To check if this is the equation of a straight line, rearrange it into the standard form of a straight line equation:<\/p>\n\n\n\n<p><strong>y = mx + c<\/strong><\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>m<\/em> is the gradient (slope) of the line<\/li>\n\n\n\n<li><em>c<\/em> is the y-intercept<\/li>\n<\/ul>\n\n\n\n<p>Starting with:<br><strong>x + 2y + 4 = 0<\/strong><\/p>\n\n\n\n<p>Subtract <em>x<\/em> and <em>4<\/em> from both sides:<br><strong>2y = -x &#8211; 4<\/strong><\/p>\n\n\n\n<p>Divide both sides by 2 to solve for <em>y<\/em>:<br><strong>y = (-1\/2)x &#8211; 2<\/strong><\/p>\n\n\n\n<p>This is now in the form <em>y = mx + c<\/em>, which is the standard equation of a straight line. Thus, the given equation represents a straight line.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">b) Find the gradient of the line<\/h3>\n\n\n\n<p>From the rearranged equation:<br><strong>y = (-1\/2)x &#8211; 2<\/strong><\/p>\n\n\n\n<p>The coefficient of <em>x<\/em> is the gradient <em>m<\/em>, so:<br><strong>Gradient (m) = -1\/2<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">c) Draw a graph of the line<\/h3>\n\n\n\n<p>To plot the graph, identify at least two points on the line:<\/p>\n\n\n\n<p><strong>Find y-intercept<\/strong><br>When <em>x = 0<\/em>:<br><strong>y = (-1\/2)(0) &#8211; 2 = -2<\/strong><br>So the point is <strong>(0, -2)<\/strong><\/p>\n\n\n\n<p><strong>Find x-intercept<\/strong><br>Set <em>y = 0<\/em>:<br><strong>0 = (-1\/2)x &#8211; 2<\/strong><br>Multiply both sides by 2:<br><strong>0 = -x &#8211; 4<\/strong><br><strong>x = -4<\/strong><br>So the point is <strong>(-4, 0)<\/strong><\/p>\n\n\n\n<p><strong>Plotting Points<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First point: <strong>(0, -2)<\/strong><\/li>\n\n\n\n<li>Second point: <strong>(-4, 0)<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Draw a straight line passing through these points. The line slopes downwards from left to right because the gradient is negative.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>The given equation is linear because it can be rearranged to the form <em>y = mx + c<\/em>, with <em>m = -1\/2<\/em> and <em>c = -2<\/em>. This form confirms that the graph is a straight line. The gradient tells us the line slopes downward at a rate of one unit down for every two units to the right. The intercepts help in sketching the graph accurately.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1237.jpeg\" alt=\"\" class=\"wp-image-40190\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1237.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1237-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1237-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A graph has the equation x + 2y + 4 = 0. a) Show that this is the equation of a straight line. b) Find the gradient of the line. c) Draw a graph of the line. The Correct Answer and Explanation is: a) Show that this is the equation of a straight line The [&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-40189","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40189","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=40189"}],"version-history":[{"count":2,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40189\/revisions"}],"predecessor-version":[{"id":40192,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40189\/revisions\/40192"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=40189"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=40189"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=40189"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}