The equation 8x + Ay = 24 represents a line with slope -4. What is the value of A?

Solve for $y$ to find the slope: $Ay = -8x + 24$, so $y = -\frac{8}{A}x + \frac{24}{A}$. The slope is $-\frac{8}{A}$. Setting it equal to $-4$ gives $\frac{8}{A} = 4$, so $A = 2$, choice A. Check: $8x + 2y = 24$ becomes $y = -4x + 12$. Choice B ($-2$) would give a slope of $+4$. Choice C (4) gives a slope of $-2$, which results from inverting the ratio. Choice D ($-4$) would give a slope of $+2$. The slope of $Bx + Ay = C$ is $-\frac{B}{A}$.