1. **State the problem:** Solve the linear equation $4x + y = 11$ for $y$ in terms of $x$. 2. **Formula and rules:** To express $y$ as a function of $x$, isolate $y$ on one side of the equation by subtracting $4x$ from both sides. 3. **Isolate $y$:** $$4x + y = 11$$ Subtract $4x$ from both sides: $$\cancel{4x} + y - \cancel{4x} = 11 - 4x$$ which simplifies to $$y = 11 - 4x$$ 4. **Interpretation:** This means for any value of $x$, $y$ can be found by subtracting $4x$ from 11. 5. **Final answer:** $$y = 11 - 4x$$