1. **State the problem:** Find the slope of the line passing through the points $(3, 8)$ and $(6, 7)$. 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 given points:** $$m = \frac{7 - 8}{6 - 3}$$ 4. **Calculate the differences:** $$m = \frac{-1}{3}$$ 5. **Simplify the fraction:** The fraction $\frac{-1}{3}$ is already in simplest form. 6. **Final answer:** The slope of the line is: $$m = -\frac{1}{3}$$