1. **State the problem:** Solve the linear equation $$-\frac{1}{5}r = 2$$ for $r$. 2. **Formula and rules:** To solve for $r$, we need to isolate $r$ by undoing the multiplication by $-\frac{1}{5}$. We do this by multiplying both sides of the equation by the reciprocal of $-\frac{1}{5}$, which is $-5$. 3. **Multiply both sides by $-5$:** $$-5 \times \left(-\frac{1}{5}r\right) = -5 \times 2$$ 4. **Simplify the left side:** $$\cancel{-5} \times \left(-\frac{1}{\cancel{5}}r\right) = -10$$ $$r = -10$$ 5. **Answer:** The solution to the equation is $$r = -10$$. This means the value of $r$ that satisfies the equation is $-10$.