A linear function q satisfies q(-1) = 12 and q(2) = 3. What is the value of q(5)?

The slope of a linear function is the change in output over the change in input: $\frac{3 - 12}{2 - (-1)} = \frac{-9}{3} = -3$. From $x = 2$ to $x = 5$ the input increases by 3, so the output changes by $-3 \times 3 = -9$. Therefore $q(5) = 3 - 9 = -6$, choice A. Choice B ($-3$) adds the slope once rather than multiplying by 3. Choice C (6) does not follow from the slope or the change in input. Choice D ($-9$) is the change in output, not the value. Always add the total change to a known output.