problem: The points $(7, -6)$ and $(-3, -4)$ are the endpoints of a diameter of a circle. What is the sum of the coordinates of the center of the circle?
solution: The midpoint of a circle's diameter is its center. Thus, the center of the circle is at $\left(\frac{7+(-3)}{2},\frac{-6+(-4)}{2}\right)=(2,-5)$. The sum of the coordinates of this point is $2+(-5)=\boxed{-3}$.