1. **State the problem:** Solve the linear equation $5x + 10y = -30$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation. Remember that you can perform the same operation on both sides of the equation to maintain equality. 3. **Isolate $y$:** $$5x + 10y = -30$$ Subtract $5x$ from both sides: $$10y = -30 - 5x$$ 4. **Divide both sides by 10 to solve for $y$:** $$y = \frac{-30 - 5x}{10}$$ 5. **Simplify the fraction:** $$y = \frac{-30}{10} - \frac{5x}{10} = -3 - \frac{1}{2}x$$ 6. **Final answer:** $$y = -3 - \frac{1}{2}x$$ This expresses $y$ in terms of $x$ for the given linear equation.