If $a$ is the $x$-intercept, $b$ is the $y$-intercept, and $m$ is the slope of the line with equation $\frac{x}4 + \frac{y}{12} = 1$, then what is the value of $a + b + m$?
To find the $x$-intercept, I need to plug in $y = 0$ and solve for $x$. Doing that, I get $\frac{x}4 + \frac{0}{12} = 1$, which simplifies to $x = 4$. So $a = 4$. To find the $y$-intercept, I need to plug in $x = 0$ and solve for $y$. Doing that, I get $\frac{0}4 + \frac{y}{12} = 1$, which simplifies to $y = 12$. So $b = 12$. To find the slope, I need to rearrange the equation into the slope-intercept form $y = mx + b$. To do that, I need to subtract $\frac{x}4$ from both sides and then multiply by $12$. Doing that, I get $y = -3x + 12$. So $m = -3$. Now I have all the values I need, so I can just add them up. $a + b + m = 4 + 12 + (-3) = 13$. 