1. **State the problem:** Find the slope of the line passing through the points $(-4, 0)$ and $(4, -2)$. 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:** Here, $x_1 = -4$, $y_1 = 0$, $x_2 = 4$, and $y_2 = -2$. $$m = \frac{-2 - 0}{4 - (-4)}$$ 4. **Simplify the denominator:** $$4 - (-4) = 4 + 4 = 8$$ So, $$m = \frac{-2}{8}$$ 5. **Simplify the fraction:** $$m = \frac{\cancel{-2}}{\cancel{8}} = \frac{-1}{4}$$ 6. **Interpretation:** The slope is $-\frac{1}{4}$, which means the line falls $1$ unit vertically for every $4$ units it moves horizontally to the right. **Final answer:** $$m = -\frac{1}{4}$$