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

The scatterplot shows the relationship between two variables, $x$ and $y$ . A line of best fit is also shown.

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

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Explanation

Choice B 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. Thus, the slope of the line of best fit shown is negative. The slope of a line passing through two 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 $left parenthesis 1 comma 12 right parenthesis$ and $left parenthesis 11 comma 4 right parenthesis$ . Substituting $left parenthesis 1 comma 12 right parenthesis$ and $left parenthesis 11 comma 4 right parenthesis$ for $left parenthesis x 1 comma y 1 right parenthesis$ and $left parenthesis x 2 comma y 2 right parenthesis$ , respectively, in $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ gives $\frac{4 - 12}{11 - 1}$ , which is equivalent to $- \frac{8}{10}$ , or $negative 0.8$ . Therefore, of the given choices, $negative 0.8$ 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 C is incorrect. The line of best fit shown has a negative slope, not a positive slope.

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