1. **State the problem:** Find the slope of the line passing through the points $(-4, 0)$ and $(0, 2)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ This formula calculates the "rise" over the "run," or how much the line goes up or down divided by how much it goes left or right. 3. **Substitute the points:** Using $(-4, 0)$ as $(x_1, y_1)$ and $(0, 2)$ as $(x_2, y_2)$, we get $$m = \frac{2 - 0}{0 - (-4)} = \frac{2}{0 + 4}$$ 4. **Simplify the denominator:** $$m = \frac{2}{\cancel{4}}$$ 5. **Final slope:** $$m = \frac{2}{4} = \frac{1}{2}$$ **Answer:** The slope of the line is $\frac{1}{2}$.