Triangle $ABC$ has vertices $A(0, 8)$, $B(2, 0)$, $C(8, 0)$.  A line through $B$ cuts the area of $\triangle ABC$ in half; find the sum of the slope and $y$-intercept of this line.
I need to find the equation of the line that passes through $B$ and divides the area of $\triangle ABC$ in half. One way to do that is to find the midpoint of $AC$, which is $D(4, 4)$, and then find the equation of the line $BD$. The slope of $BD$ is $\frac{4 - 0}{4 - 2} = 2$. The $y$-intercept of $BD$ is $b$ such that $0 = 2 \cdot 2 + b$, so $b = -4$. The equation of $BD$ is $y = 2x - 4$. The sum of the slope and $y$-intercept of this line is $2 + (-4) = -2$. 