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) $. The midpoint of the first segment is $ \left(\frac{0+2}{2}, \frac{0+2}{2}\right) = (1,1) $ and the midpoint of the second segment is $ \left(\frac{5+6}{2}, \frac{0+2}{2}\right) = (5.5,1) $. Since the $ y $-coordinates are the same, the line is horizontal. All horizontal lines have a slope of $ \boxed{0} $.