1. **State the problem:** Determine the slope of line CD given points C(3, -6) and D(-2, 4). 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope of CD:** $$m = \frac{4 - (-6)}{-2 - 3} = \frac{4 + 6}{-5} = \frac{10}{-5}$$ 4. **Simplify the fraction:** $$m = \frac{\cancel{10}}{\cancel{5} \times 2} = -2$$ 5. **Answer:** The slope of line CD is $-2$. --- 6. **Translate points C and D right 5 units:** - For point C(3, -6), new coordinates are $C' = (3 + 5, -6) = (8, -6)$. - For point D(-2, 4), new coordinates are $D' = (-2 + 5, 4) = (3, 4)$. 7. **Calculate the slope of line C'D':** $$m' = \frac{4 - (-6)}{3 - 8} = \frac{10}{-5} = -2$$ 8. **Relationship between lines CD and C'D':** Since both slopes are equal ($-2$), lines CD and C'D' are parallel. **Final answers:** - Slope of CD: $-2$ - Coordinates of $C'$: $(8, -6)$ - Coordinates of $D'$: $(3, 4)$ - Slope of $C'D'$: $-2$ - Lines CD and C'D' are parallel because they have the same slope.