{"id":33045,"date":"2025-06-23T05:41:51","date_gmt":"2025-06-23T05:41:51","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=33045"},"modified":"2025-06-23T05:41:52","modified_gmt":"2025-06-23T05:41:52","slug":"10-8-6-4-2-0-2-4-6-8-10-10-y-8-6-4-2-0-2-4-6-8-10-x","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/10-8-6-4-2-0-2-4-6-8-10-10-y-8-6-4-2-0-2-4-6-8-10-x\/","title":{"rendered":"-10 -8 -6 -4 -2 0 2 4 6 8 10 10 y 8 6 4 2 0 -2 -4 -6 -8 -10 x"},"content":{"rendered":"\n<p>-10 -8 -6 -4 -2 0 2 4 6 8 10 10 y 8 6 4 2 0 -2 -4 -6 -8 -10 x<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"289\" height=\"290\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-233.png\" alt=\"\" class=\"wp-image-33046\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-233.png 289w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-233-150x150.png 150w\" sizes=\"auto, (max-width: 289px) 100vw, 289px\" \/><\/figure>\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<p>The graph shows a straight line passing through the coordinate plane. By observing its key intercepts, we can determine its equation.<\/p>\n\n\n\n<p>The line crosses the y-axis at the point (0, 2) and the x-axis at approximately (\u20132, 0). From these two points, we can calculate the slope mm using the slope formula:<\/p>\n\n\n\n<p>m=y2\u2212y1x2\u2212x1=0\u22122\u22122\u22120=\u22122\u22122=1m = \\frac{y_2 &#8211; y_1}{x_2 &#8211; x_1} = \\frac{0 &#8211; 2}{-2 &#8211; 0} = \\frac{-2}{-2} = 1<\/p>\n\n\n\n<p>Now that we know the slope is 1 and the y-intercept is 2, we can write the equation of the line in slope-intercept form y=mx+by = mx + b:<\/p>\n\n\n\n<p>y=x+2y = x + 2<\/p>\n\n\n\n<p><strong>Explanation<\/strong><\/p>\n\n\n\n<p>The equation y=x+2y = x + 2 represents a linear function, one whose graph is a straight line. Every linear function has a constant rate of change, known as its slope. Here, the slope is 1, which means that for each unit increase in x, the y-value increases by the same amount. This gives the line a consistent rise over run of 1, making it ascend diagonally from left to right at a 45-degree angle.<\/p>\n\n\n\n<p>The y-intercept, which is the point where the line crosses the vertical y-axis, occurs at (0, 2). This tells us that when no input (x = 0) is applied to the function, the output (y) is 2. The x-intercept, where the line crosses the horizontal x-axis, is at approximately (\u20132, 0). This occurs when the output value y is zero, giving us a helpful verification of the equation since plugging \u20132 into the equation yields y=\u20132+2=0y = \u20132 + 2 = 0.<\/p>\n\n\n\n<p>This linear graph divides the coordinate plane into two regions. Points above the line satisfy the inequality y&gt;x+2y &gt; x + 2, while points below satisfy y&lt;x+2y &lt; x + 2. Because the slope is positive, the function is increasing, meaning the function outputs grow as the input increases.<\/p>\n\n\n\n<p>The consistent pattern, symmetry, and predictable growth make this line a clear example of a linear relationship in algebra.<\/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-banner8-482.jpeg\" alt=\"\" class=\"wp-image-33047\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-482.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-482-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-482-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>-10 -8 -6 -4 -2 0 2 4 6 8 10 10 y 8 6 4 2 0 -2 -4 -6 -8 -10 x The Correct Answer and Explanation is: The graph shows a straight line passing through the coordinate plane. By observing its key intercepts, we can determine its equation. The line crosses 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-33045","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33045","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=33045"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33045\/revisions"}],"predecessor-version":[{"id":33048,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33045\/revisions\/33048"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=33045"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=33045"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=33045"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}