1. **State the problem:** Find the slope of the line passing through the points $(6,4)$ and $(-3,-2)$. 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 given points:** Let $(x_1,y_1) = (-3,-2)$ and $(x_2,y_2) = (6,4)$. $$m = \frac{4 - (-2)}{6 - (-3)} = \frac{4 + 2}{6 + 3} = \frac{6}{9}$$ 4. **Simplify the fraction:** $$m = \frac{6}{9} = \frac{\cancel{3} \times 2}{\cancel{3} \times 3} = \frac{2}{3}$$ 5. **Interpretation:** The slope of the line is $\frac{2}{3}$, which means for every 3 units moved horizontally to the right, the line rises 2 units vertically. **Final answer:** $$m = \frac{2}{3}$$