1. **State the problem:** Solve the equation $2x + 2y = 32$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we use basic algebraic operations: subtraction and division. 3. **Isolate $y$:** $$2x + 2y = 32$$ Subtract $2x$ from both sides: $$2y = 32 - 2x$$ 4. **Divide both sides by 2:** $$y = \frac{32 - 2x}{2}$$ Simplify the right side: $$y = 16 - x$$ 5. **Interpretation:** The equation $y = 16 - x$ represents a line where for every increase of 1 in $x$, $y$ decreases by 1, and when $x=0$, $y=16$. **Final answer:** $$y = 16 - x$$