1. **State the problem:** Find the slope of the line passing through the points (2,3) and (5,7). 2. **Formula:** The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ This formula calculates the "rise" over the "run" or the change in $y$ divided by the change in $x$. 3. **Substitute the values:** $$m = \frac{7 - 3}{5 - 2}$$ 4. **Simplify:** $$m = \frac{4}{3}$$ 5. **Interpretation:** The slope of the line through points (2,3) and (5,7) is $\frac{4}{3}$. This means for every 3 units moved horizontally to the right, the line rises 4 units vertically. Hence, the slope $m = \frac{4}{3}$.