jmc

The midpoint of a line segment with endpoints $(x_1,y_1),(x_2,y_2)$ is $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$, which should make sense since the midpoint is halfway between the endpoints. So the midpoint of the first segment is $\left(\frac{0+2}{2},\frac{0+3}{2}\right)=(1,1.5)$ and the midpoint of the second segment is $\left(\frac{5+6}{2},\frac{0+3}{2}\right)=(5.5,1.5)$. Note that the slope of the desired line must then be $\boxed{0}$, since the $y$-coordinates of the two points are the same.