The equation 6x + Ay = 18 represents a line with slope -2. What is the value of A?

Solve for $y$ to find the slope. From $6x + Ay = 18$, we get $Ay = -6x + 18$, so $y = -\frac{6}{A}x + \frac{18}{A}$. The slope is $-\frac{6}{A}$. Setting $-\frac{6}{A} = -2$ gives $6 = 2A$ and $A = 3$, choice A. Check: $6x + 3y = 18$ becomes $y = -2x + 6$, with slope $-2$. Choice B (9) gives slope $-\frac{2}{3}$. Choice C ($-3$) would give slope $+2$. Choice D ($-9$) gives slope $+\frac{2}{3}$. The slope formula for $Bx + Ay = C$ is $-\frac{B}{A}$.