Two-variable data: Models and scatterplots SAT question

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, $(x_1,y_1)$ and $(x_2,y_2)$, can be calculated as $\frac{y_2-y_1}{x_2-x_1}$. The line of best fit shown passes approximately through the points $(1,12)$ and $(11,4)$. Substituting $(1,12)$ and $(11,4)$ for $(x_1,y_1)$ and $(x_2,y_2)$, 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 $-0.8$. Therefore, of the given choices, $-0.8$ 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.