1. **Problem:** Find the slope of the line through points (2,3) and (4,9). 2. **Formula:** 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. **Apply the formula:** $$m=\frac{9-3}{4-2}=\frac{6}{2}$$ 4. **Simplify the fraction:** $$m=\frac{\cancel{6}}{\cancel{2}}=3$$ 5. **Explanation:** The slope is the ratio of the vertical change to the horizontal change between two points. Here, the vertical change is 6 and the horizontal change is 2, so the slope is 3. **Final answer:** The slope of the line through (2,3) and (4,9) is **3**.