1. **Problem Statement:** We are given that line X contains the hypotenuses of two similar triangles LMN and PQR. The slope of line X between points (-7, 6) and (-4, 4) is given as $-\frac{2}{3}$. We need to find the slope of line X between points (-1, 2) and (5, -2). 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ This formula calculates the "rise over run," or the change in $y$ divided by the change in $x$. 3. **Calculate the slope between (-1, 2) and (5, -2):** $$ m = \frac{-2 - 2}{5 - (-1)} = \frac{-4}{6} = -\frac{2}{3} $$ 4. **Interpretation:** The slope between (-1, 2) and (5, -2) is $-\frac{2}{3}$, which matches the slope given for the segment between (-7, 6) and (-4, 4). 5. **Conclusion:** Since the hypotenuse lies on the same line X, the slope must be consistent along the line. Therefore, the slope between (-1, 2) and (5, -2) is also $-\frac{2}{3}$. **Final answer:** A. $-\frac{2}{3}$