The sterplot has 10 data points. The data points are in a linear pattern trending up from left to right.

Question

The sterplot shows the relationship between two variables, $x$ and $y$ , for data set E. A line of best fit is shown. Data set F is created by multiplying the y-coordinate of each data point from data set E by $3.9$ . Which of the following could be an equation of a line of best fit for data set F?

Accepted Answer

Choice A is correct. An equation of a line of best fit for data set F can be written in the form y = a + b x , where a is the y -coordinate of the y -intercept of the line of best fit and b is the slope. The line of best fit shown for data set E has a y -intercept at approximately 0 , 12 . It's given that data set F is created by multiplying the y -coordinate of each data point from data set E by 3.9 . It follows that a line of best fit for data set F has a y -intercept at approximately 0 , 12 3.9 , or 0 , 46.8 . Therefore, the value of a is approximately 46.8 . The slope of a line that passes through points x 1 , y 1 and x 2 , y 2 can be calculated as y 2 - y 1 x 2 - x 1 . Since the line of best fit shown for data set E passes approximately through the point 12 , 30 , it follows that a line of best fit for data set F passes approximately through the point 12 , 30 3.9 , or 12 , 117 . Substituting 0 , 46.8 and 12 , 117 for x 1 , y 1 and x 2 , y 2 , respectively, in y 2 - y 1 x 2 - x 1 yields 117 - 46.8 12 - 0 , which is equivalent to 70.2 12 , or 5.85 . Therefore, the value of b is approximately 5.85 , or approximately 5.9 . Thus, y = 46.8 + 5.9 x could be an equation of a line of best fit for data set F. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This could be an equation of a line of best fit for data set E, not data set F.

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