1. **State the problem:** Find the slope of the line passing through the points $(-4, 5)$ and $(2, -1)$. 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:** Here, $(x_1, y_1) = (-4, 5)$ and $(x_2, y_2) = (2, -1)$. So, $$m = \frac{-1 - 5}{2 - (-4)}$$ 4. **Simplify numerator and denominator:** $$m = \frac{-6}{2 + 4}$$ 5. **Simplify denominator:** $$m = \frac{-6}{6}$$ 6. **Simplify the fraction by canceling common factors:** $$m = \frac{\cancel{-6}}{\cancel{6}} = -1$$ 7. **Conclusion:** The slope of the line is $-1$. **Final answer:** $-1$ (Option A)