1. **State the problem:** We have a rhombus, and the slope of one diagonal is $\frac{2}{3}$. We need to find the slope of the other diagonal. 2. **Recall properties of a rhombus:** The diagonals of a rhombus are perpendicular to each other. 3. **Use the perpendicular slope rule:** If two lines are perpendicular, the product of their slopes is $-1$. 4. **Set up the equation:** Let the slope of the other diagonal be $m$. Then: $$\frac{2}{3} \times m = -1$$ 5. **Solve for $m$:** $$m = \frac{-1}{\frac{2}{3}} = -1 \times \frac{3}{2} = -\frac{3}{2}$$ 6. **Simplify and interpret:** The slope of the other diagonal is $-\frac{3}{2}$. Among the given options, $-\frac{3}{2}$ is not listed, but the closest equivalent slope is $-\frac{3}{2}$ which is not in the options. However, since the slope of one diagonal is $\frac{2}{3}$, the perpendicular slope must be $-\frac{3}{2}$, which is the negative reciprocal. 7. **Check options:** The options are $-\frac{2}{3}$, $-\frac{1}{2}$, $\frac{2}{3}$, and $\frac{1}{2}$. None match $-\frac{3}{2}$. The correct slope is $-\frac{3}{2}$, so none of the options are correct as given. **Final answer:** The slope of the other diagonal is $-\frac{3}{2}$, the negative reciprocal of $\frac{2}{3}$.