1. **State the problem:** Find the slope of the line passing through the points (0, 4), (1, 2), and (-1, 6). 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate slope between points (0, 4) and (1, 2):** $$m = \frac{2 - 4}{1 - 0} = \frac{-2}{1} = -2$$ 4. **Calculate slope between points (0, 4) and (-1, 6):** $$m = \frac{6 - 4}{-1 - 0} = \frac{2}{-1} = -2$$ 5. Since the slope between both pairs of points is the same, the slope of the line is consistent and equals $-2$. **Final answer:** The slope of the line is $-2$.