1. **State the problem:** Find the slope of the line passing through the points $(-4, -1)$ and $(4, 5)$. 2. **Formula for slope:** The slope $m$ of a line through 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:** $$m = \frac{5 - (-1)}{4 - (-4)}$$ 4. **Simplify the numerator and denominator:** $$m = \frac{5 + 1}{4 + 4}$$ 5. **Calculate the values:** $$m = \frac{6}{8}$$ 6. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor 2:** $$m = \frac{\cancel{6}^3}{\cancel{8}^4} = \frac{3}{4}$$ 7. **Interpretation:** The slope of the line is $\frac{3}{4}$, meaning for every 4 units moved horizontally to the right, the line rises 3 units vertically. **Final answer:** $$m = \frac{3}{4}$$