{"id":28324,"date":"2025-06-20T11:45:17","date_gmt":"2025-06-20T11:45:17","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=28324"},"modified":"2025-06-20T11:45:27","modified_gmt":"2025-06-20T11:45:27","slug":"find-a-linear-model-for-the-above-data-using-the-points-0344-3-and-22380-9","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-a-linear-model-for-the-above-data-using-the-points-0344-3-and-22380-9\/","title":{"rendered":"Find a linear model for the above data using the points (0,344.3) and (22,380.9)"},"content":{"rendered":"\n<p>Find a linear model for the above data using the points (0,344.3) and (22,380.9).<\/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 a <strong>linear model<\/strong> based on the two points:<br><strong>(0, 344.3)<\/strong> and <strong>(22, 380.9)<\/strong>,<br>we will follow the standard form 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>,<\/li>\n\n\n\n<li>bb is the <strong>y-intercept<\/strong>.<\/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\"><strong>Step 1: Find the slope (m)<\/strong><\/h3>\n\n\n\n<p>The slope formula between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is: m=y2\u2212y1x2\u2212x1m = \\frac{y_2 &#8211; y_1}{x_2 &#8211; x_1}<\/p>\n\n\n\n<p>Substitute the values: m=380.9\u2212344.322\u22120=36.622\u22481.6636m = \\frac{380.9 &#8211; 344.3}{22 &#8211; 0} = \\frac{36.6}{22} \\approx 1.6636<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Find the y-intercept (b)<\/strong><\/h3>\n\n\n\n<p>We use one point (e.g., (0, 344.3)) and the slope to solve for bb: y=mx+b\u21d2344.3=(1.6636)(0)+b\u21d2b=344.3y = mx + b \\Rightarrow 344.3 = (1.6636)(0) + b \\Rightarrow b = 344.3<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Final Linear Model<\/strong><\/h3>\n\n\n\n<p>y=1.6636x+344.3y = 1.6636x + 344.3<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300 words)<\/strong><\/h3>\n\n\n\n<p>A <strong>linear model<\/strong> helps describe a straight-line relationship between two variables. In this case, the data is represented by two specific points: (0, 344.3) and (22, 380.9). These points can be interpreted as coordinates on a graph where the x-values represent an independent variable (like time, years, or quantity), and the y-values represent a dependent variable (like cost, temperature, or population).<\/p>\n\n\n\n<p>To build a linear model, we first calculated the <strong>slope (rate of change)<\/strong> using the difference in y-values over the difference in x-values. This gives us how much the dependent variable increases for every one-unit increase in the independent variable. Here, the slope m=1.6636m = 1.6636 tells us that for each increase of 1 in x, y increases by about 1.66.<\/p>\n\n\n\n<p>Next, we found the <strong>y-intercept (b)<\/strong>, which is the value of y when x = 0. From the point (0, 344.3), it is clear that the y-intercept is 344.3. This serves as the starting value of the model when the independent variable is zero.<\/p>\n\n\n\n<p>Therefore, the linear equation y=1.6636x+344.3y = 1.6636x + 344.3 allows us to predict values of y for any x. This type of model is commonly used in forecasting, business, science, and economics because it simplifies complex relationships into manageable, predictable forms.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find a linear model for the above data using the points (0,344.3) and (22,380.9). The correct answer and explanation is: To find a linear model based on the two points:(0, 344.3) and (22, 380.9),we will follow the standard form of a linear equation: y=mx+by = mx + b Where: Step 1: Find the slope (m) [&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-28324","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28324","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=28324"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28324\/revisions"}],"predecessor-version":[{"id":28331,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28324\/revisions\/28331"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=28324"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=28324"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=28324"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}