1. **State the problem:** Find the slope $m$ of the line passing through points $(1,7)$ and $(2,10)$. 2. **Formula:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line. 3. **Substitute values:** Using $(x_1, y_1) = (1,7)$ and $(x_2, y_2) = (2,10)$, we get $$m = \frac{10 - 7}{2 - 1}$$ 4. **Simplify:** Calculate numerator and denominator: $$m = \frac{3}{1}$$ 5. **Final answer:** The slope in simplest form is $$m = 3$$ This means the line rises 3 units vertically for every 1 unit it moves horizontally.