1. **State the problem:** Solve for $y$ in the equation $y + 3 = -\frac{1}{5}(x - 4)$. 2. **Use the distributive property:** Apply the distributive property to the right side: $$y + 3 = -\frac{1}{5}x + \frac{4}{5}$$ 3. **Isolate $y$:** Subtract 3 from both sides to solve for $y$: $$y = -\frac{1}{5}x + \frac{4}{5} - 3$$ 4. **Simplify the constant term:** Convert 3 to a fraction with denominator 5: $$3 = \frac{15}{5}$$ 5. **Combine the fractions:** $$y = -\frac{1}{5}x + \frac{4}{5} - \frac{15}{5} = -\frac{1}{5}x - \frac{11}{5}$$ **Final answer:** $$y = -\frac{1}{5}x - \frac{11}{5}$$