The equation Ax + 4y = 12 represents a line with slope -3/2. What is the value of A?

Put $Ax + 4y = 12$ in slope-intercept form: $4y = -Ax + 12$, so $y = -\frac{A}{4}x + 3$. The slope is $-\frac{A}{4}$. Setting it equal to $-\frac{3}{2}$ gives $\frac{A}{4} = \frac{3}{2}$, so $A = 6$, choice A. Choice B ($-6$) comes from keeping the negative sign when it should cancel. Choice C (3) equates $A$ with the numerator of the slope and ignores the 4. Choice D (8) does not give the right slope, since $-\frac{8}{4} = -2$. The general formula for $Ax + By = C$ is slope $= -\frac{A}{B}$.