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: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Substitute the values:** $$m = \frac{7 - 3}{5 - 2}$$ 4. **Simplify the numerator and denominator:** $$m = \frac{4}{3}$$ 5. **Interpretation:** The slope of the line between the points $(2,3)$ and $(5,7)$ is $\frac{4}{3}$, meaning for every 3 units increase in $x$, $y$ increases by 4 units.