Which of the following could be the equation for a line of best fit for the data shown in the

Question

Which of the following could be the equation for a line of best fit for the data shown in the sterplot above?

Accepted Answer

Choice A is correct. The data show a strong linear relationship between x and y . The line of best fit for a set of data is a linear equation that minimizes the distances from the data points to the line. An equation for the line of best fit can be written in slope-intercept form, , where m is the slope of the graph of the line and b is the y -coordinate of the y -intercept of the graph. Since, for the data shown, the y -values increase as the x -values increase, the slope of a line of best fit must be positive. The data shown lie almost in a line, so the slope can be roughly estimated using the formula for slope, . The leftmost and rightmost data points have coordinates of about and , so the slope is approximately , which is a little greater than 3. Extension of the line to the left would intersect the y -axis at about . Only choice A represents a line with a slope close to 3 and a y -intercept close to . Choice B is incorrect and may result from switching the slope and y -intercept. The line with a y -intercept of and a slope of 0.8 is farther from the data points than the line with a slope of 3 and a y -intercept of . Choices C and D are incorrect. They represent lines with negative slopes, not positive slopes.

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