1. **State the problem:** Solve the equation $-10x + 8y = 0$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation. 3. **Intermediate work:** Start with the equation: $$-10x + 8y = 0$$ Add $10x$ to both sides: $$8y = 10x$$ Divide both sides by 8: $$y = \frac{10x}{8}$$ Simplify the fraction: $$y = \frac{5x}{4}$$ 4. **Explanation:** We moved the $-10x$ term to the right side by adding $10x$ to both sides. Then, to isolate $y$, we divided both sides by 8. Simplifying the fraction gives the final expression for $y$ in terms of $x$. **Final answer:** $$y = \frac{5x}{4}$$