Two-variable data: Models and scatterplots SAT question

Choice D is correct. The data points suggest that as the variable $x$ increases, the variable $y$ decreases, which implies that an appropriate linear model for the data has a negative slope. The data points also show that when $x$ is close to $0$, $y$ is greater than $9$. Therefore, the y-intercept of the graph of an appropriate linear model has a y-coordinate greater than $9$. The graph of an equation of the form $y=a+bx$, where $a$ and $b$ are constants, has a y-intercept with a y-coordinate of $a$ and has a slope of $b$. Of the given choices, only choice D represents a graph that has a negative slope, $-0.9$, and a y-intercept with a y-coordinate greater than $9$, $9.4$.

Choice A is incorrect. The graph of this equation has a positive slope, not a negative slope, and a y-intercept with a y-coordinate less than $1$, not greater than $9$.

Choice B is incorrect. The graph of this equation has a y-intercept with a y-coordinate less than $1$, not greater than $9$.

Choice C is incorrect. The graph of this equation has a positive slope, not a negative slope.