1. **State the problem:** Solve the linear equation $-x + 2y = 6$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by performing algebraic operations. 3. **Isolate $y$:** Starting with $$-x + 2y = 6$$ add $x$ to both sides: $$\cancel{-x} + 2y = 6 + \cancel{x} \implies 2y = x + 6$$ 4. **Divide both sides by 2:** $$y = \frac{x + 6}{2}$$ 5. **Simplify the fraction:** $$y = \frac{x}{2} + \frac{6}{2} = \frac{x}{2} + 3$$ 6. **Final answer:** $$y = \frac{x}{2} + 3$$ This expresses $y$ as a function of $x$.