1. **State the problem:** Find the slope of the line passing through the points $(0,0)$ and $(3,2)$. 2. **Formula for slope:** The slope $m$ of a line passing 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:** Using points $(0,0)$ and $(3,2)$: $$m = \frac{2 - 0}{3 - 0} = \frac{2}{3}$$ 4. **Check with another point:** The line also passes through $(6,4)$. Calculate slope between $(3,2)$ and $(6,4)$: $$m = \frac{4 - 2}{6 - 3} = \frac{2}{3}$$ 5. **Conclusion:** The slope is consistent and equals $\frac{2}{3}$. **Final answer:** The slope of the line is $\frac{2}{3}$.