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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 this line of best fit?

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Explanation

Choice C is correct. A line of best fit is shown in the scatterplot such that as the value of $x$ increases, the value of $y$ decreases. It follows that the slope of the line of best fit shown is negative. The slope of a line in the xy-plane that passes through the points $left parenthesis x 1 comma y 1 right parenthesis$ and $left parenthesis x 2 comma y 2 right parenthesis$ can be calculated as $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ . The line of best fit shown passes approximately through the points $left parenthesis 0 comma 8 right parenthesis$ and $left parenthesis 10 comma 1 right parenthesis$ . Substituting $left parenthesis 0 comma 8 right parenthesis$ for $left parenthesis x 1 comma y 1 right parenthesis$ and $left parenthesis 10 comma 1 right parenthesis$ for $left parenthesis x 2 comma y 2 right parenthesis$ in $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ yields the slope of the line being approximately $\frac{1 - 8}{10 - 0}$ , which is equivalent to $\frac{- 7}{10}$ , or $negative 0.7$ . Therefore, of the given choices, $negative 0.7$ is the closest to the slope of this line of best fit.

Choice A is incorrect. The line of best fit shown has a negative slope, not a positive slope.

Choice B is incorrect. The line of best fit shown has a negative slope, not a positive slope.

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