1. **State the problem:** Solve the linear equation $4x + y = 8$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, subtract $4x$ from both sides of the equation. 3. **Intermediate work:** $$4x + y = 8$$ Subtract $4x$ from both sides: $$\cancel{4x} + y - \cancel{4x} = 8 - 4x$$ Simplifies to: $$y = 8 - 4x$$ 4. **Explanation:** We moved the term $4x$ to the right side by subtracting it from both sides, leaving $y$ alone on the left side. This gives the expression for $y$ in terms of $x$. **Final answer:** $$y = 8 - 4x$$