1. **State the problem:** Find the slope of a line perpendicular to the line passing through points (9, 0) and (10, 7). 2. **Find the slope of the original line:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1) = (9, 0)$ and $(x_2, y_2) = (10, 7)$. 3. **Calculate the slope:** $$m = \frac{7 - 0}{10 - 9} = \frac{7}{1} = 7$$ 4. **Find the slope of the perpendicular line:** The slope of a line perpendicular to another is the negative reciprocal of the original slope. 5. **Calculate the perpendicular slope:** $$m_{\perp} = -\frac{1}{7}$$ 6. **Final answer:** The slope of the line perpendicular to the line through (9, 0) and (10, 7) is $$m = -\frac{1}{7}$$.