1. **State the problem:** Find the slope of the line passing through the points $(-7, 2)$ and $(9, 6)$. 2. **Formula:** The slope $m$ of a line passing 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:** $$m = \frac{6 - 2}{9 - (-7)}$$ 4. **Simplify the numerator and denominator:** $$m = \frac{4}{9 + 7}$$ 5. **Add the denominator:** $$m = \frac{4}{16}$$ 6. **Simplify the fraction:** $$m = \frac{1}{4}$$ **Final answer:** The slope of the line passing through the points $(-7, 2)$ and $(9, 6)$ is $\frac{1}{4}$.