1. **Problem statement:** We are given points $C(3, -6)$ and $D(-2, 4)$. 2. **Find the slope of line $CD$:** The slope formula is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1) = (3, -6)$ and $(x_2, y_2) = (-2, 4)$. 3. **Calculate the slope:** $$m = \frac{4 - (-6)}{-2 - 3} = \frac{4 + 6}{-5} = \frac{10}{-5}$$ 4. **Simplify the fraction:** $$m = \frac{\cancel{10}^{2 \times 5}}{\cancel{-5}^{-1 \times 5}} = -2$$ 5. **Translate points $C$ and $D$ right 5 units to get $C'$ and $D'$:** Translation right 5 units means adding 5 to the $x$-coordinates. $$C' = (3 + 5, -6) = (8, -6)$$ $$D' = (-2 + 5, 4) = (3, 4)$$ 6. **Find the slope of line $C'D'$:** Using the slope formula again with $C'(8, -6)$ and $D'(3, 4)$: $$m' = \frac{4 - (-6)}{3 - 8} = \frac{10}{-5} = -2$$ 7. **Relationship between lines $CD$ and $C'D'$:** Both lines have the same slope $-2$, so they are parallel. Translation does not change the slope, only shifts the line horizontally. **Final answers:** - Slope of $CD$ is $-2$. - Coordinates of $C'$ and $D'$ are $(8, -6)$ and $(3, 4)$ respectively. - Slope of $C'D'$ is $-2$. - Lines $CD$ and $C'D'$ are parallel because they have the same slope.