1. **State the problem:** Find the slope of the line passing through the points $(1, 9)$ and $(8, 8)$. 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:** $$m = \frac{8 - 9}{8 - 1}$$ 4. **Calculate the numerator and denominator:** $$m = \frac{-1}{7}$$ 5. **Simplify the fraction:** The fraction $\frac{-1}{7}$ is already in simplest form. 6. **Final answer:** $$m = -\frac{1}{7}$$ The slope of the line passing through $(1, 9)$ and $(8, 8)$ is $-\frac{1}{7}$.