1. **State the problem:** Solve the linear equation for $y$ given the equation $-5x + y = -7$. 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: $$\cancel{-5x} + y + 5x = -7 + 5x$$ which simplifies to $$y = 5x - 7$$ 4. **Explanation:** We moved $-5x$ to the right side by adding $5x$ to both sides, which cancels it on the left. This leaves $y$ alone on the left side, giving the solution for $y$ in terms of $x$. **Final answer:** $$y = 5x - 7$$