jmc

We can find the $x$-intercept by setting $y=0$ in the equation. This gives us $\frac{x}{4}=1$, so $x=4$, which means $a=4$. Similarly, letting $x=0$ gives $\frac{y}{12}=1$, so $y=12$, which means $b=12$. There are several ways we can find the slope. First, we could put the equation in slope-intercept form by subtracting $\frac{x}{4}$ from both sides, and then multiplying by 12. This gives $y=-3x+12$, which tells us that the slope is $-3$ (and confirms our solution for the $y$-intercept). We also could have noted that since we have already shown that $(4,0)$ and $(0,12)$ are on the line, the slope of the line is $\frac{12-0}{0-4}=-3$. Therefore, the desired sum is $4+12-3=\boxed{13}$.