1. **State the problem:** Find the slope of the line passing through the points $(-2, 5)$ and $(4, -1)$. 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. **Substitute the given points:** $$m = \frac{-1 - 5}{4 - (-2)}$$ 4. **Simplify the numerator and denominator:** $$m = \frac{-6}{4 + 2}$$ 5. **Simplify the denominator:** $$m = \frac{-6}{6}$$ 6. **Cancel common factors:** $$m = \frac{\cancel{-6}}{\cancel{6}} = -1$$ 7. **Interpretation:** The slope of the line through the points $(-2, 5)$ and $(4, -1)$ is $-1$. **Final answer:** $-1$ (Option A).