1. **State the problem:** Find the slope of the line passing through the points $(-2, -2)$ and $(1, 4)$.\n\n2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:\n$$m = \frac{y_2 - y_1}{x_2 - x_1}$$\n\n3. **Substitute the given points:**\n$$m = \frac{4 - (-2)}{1 - (-2)}$$\n\n4. **Simplify the numerator and denominator:**\n$$m = \frac{4 + 2}{1 + 2}$$\n\n5. **Calculate the sums:**\n$$m = \frac{6}{3}$$\n\n6. **Simplify the fraction by canceling common factors:**\n$$m = \frac{\cancel{6}}{\cancel{3}} = 2$$\n\n7. **Interpretation:** The slope of the line is $2$, which means the line rises 2 units vertically for every 1 unit it moves horizontally to the right.