1. **State the problem:** We are given two lines, line c with slope $\frac{85}{82}$ and line d with slope $-\frac{82}{85}$. We need to determine if these lines are parallel, perpendicular, or neither. 2. **Recall the rules:** - Two lines are **parallel** if their slopes are equal. - Two lines are **perpendicular** if the product of their slopes is $-1$. 3. **Calculate the product of the slopes:** $$\frac{85}{82} \times \left(-\frac{82}{85}\right) = -\frac{85 \times 82}{82 \times 85}$$ 4. **Simplify the fraction:** $$-\frac{\cancel{85} \times \cancel{82}}{\cancel{82} \times \cancel{85}} = -1$$ 5. **Interpret the result:** Since the product of the slopes is $-1$, the lines are **perpendicular**. **Final answer:** Line c and line d are perpendicular.