A linear function s satisfies s(-2) = 15 and s(3) = 0. What is the value of s(7)?

Find the slope: $\frac{0 - 15}{3 - (-2)} = \frac{-15}{5} = -3$. From $x = 3$ to $x = 7$, the input increases by 4, so the output changes by $-3 \times 4 = -12$. Then $s(7) = 0 - 12 = -12$, choice A. Choice B ($-9$) uses a change in $x$ of 3 instead of 4. Choice C (12) has the wrong sign, from using a slope of $+3$. Choice D ($-15$) is the change from $x = -2$ to $x = 3$ in reverse, and not the value at 7. Multiply the slope by the full change in $x$.