1. **Stating the problem:** Solve the equation for $y$ given the linear equation $-x + 3y = 0$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by performing algebraic operations such as addition, subtraction, multiplication, or division. 3. **Isolate $y$:** $$-x + 3y = 0$$ Add $x$ to both sides: $$-x + 3y + x = 0 + x$$ $$3y = x$$ 4. **Divide both sides by 3 to solve for $y$:** $$y = \frac{x}{3}$$ 5. **Intermediate step showing cancellation:** $$y = \frac{\cancel{3}y}{\cancel{3}} = \frac{x}{3}$$ 6. **Final answer:** $$y = \frac{x}{3}$$ This means for any value of $x$, $y$ is one third of $x$.