1. **State the problem:** Solve the linear equation $-5x + y = -7$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by adding or subtracting terms. 3. **Isolate $y$:** $$-5x + y = -7$$ Add $5x$ to both sides: $$\cancel{-5x} + y + 5x = -7 + 5x$$ $$y = 5x - 7$$ 4. **Explanation:** We moved $-5x$ to the right side by adding $5x$ to both sides, which cancels out $-5x$ on the left. This leaves $y$ alone on the left side, giving the solution $y = 5x - 7$. **Final answer:** $$y = 5x - 7$$