1. **State the problem:** Find the slope of the line passing through the points $(-6, 0)$ and $(-3, -3)$. 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 points:** Here, $(x_1, y_1) = (-6, 0)$ and $(x_2, y_2) = (-3, -3)$. So, $$m = \frac{-3 - 0}{-3 - (-6)} = \frac{-3}{-3 + 6}$$ 4. **Simplify the denominator:** $$m = \frac{-3}{3}$$ 5. **Simplify the fraction:** $$m = \frac{\cancel{-3}}{\cancel{3}} = -1$$ 6. **Interpretation:** The slope is $-1$, which means the line goes down one unit vertically for every one unit it moves horizontally to the right. **Final answer:** The slope of the line is $-1$.