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Problem-Solving and Data Analysis / Two-variable data: Models and scatterplots Difficulty: Medium

In the given scatterplot, a line of best fit for the data is shown.

Which of the following is closest to the slope of the line of best fit shown?

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Explanation

Choice D is correct. A line in the xy-plane that passes through the points $left parenthesis x 1 comma y 1 right parenthesis$ and $left parenthesis x 2 comma y 2 right parenthesis$ has a slope of $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ . The line of best fit shown passes approximately through the points $left parenthesis 1 comma 3.3 right parenthesis$ and $left parenthesis 7 comma 14.5 right parenthesis$ . It follows that the slope of this best fit line is approximately $\frac{14.5 - 3.3}{7 - 1}$ , which is equivalent to $StartFraction 11.2 Over 6 EndFraction$ , or approximately $1.87$ . Therefore, of the given choices, $2$ is closest to the slope of the line of best fit shown.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.