1. **State the problem:** Find the slope of the line passing through the points $(-9, -10)$ and $(7, 7)$. 2. **Formula for slope:** The slope $m$ of a line 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 points:** $$m = \frac{7 - (-10)}{7 - (-9)} = \frac{7 + 10}{7 + 9} = \frac{17}{16}$$ 4. **Simplify the fraction:** Since 17 and 16 have no common factors other than 1, the slope in simplest form is $$m = \frac{17}{16}$$ 5. **Interpretation:** The "rise" is 17 units (change in $y$), and the "run" is 16 units (change in $x$). This means for every 16 units moved horizontally, the line rises 17 units vertically. **Final answer:** The slope of the line is $\frac{17}{16}$.