1. **State the problem:** Solve the linear equation $85x + 58.5y = 9.7$ for one variable in terms of the other. 2. **Formula and rules:** This is a linear equation in two variables. To express $y$ in terms of $x$, isolate $y$ on one side. 3. **Isolate $y$:** $$85x + 58.5y = 9.7$$ Subtract $85x$ from both sides: $$58.5y = 9.7 - 85x$$ 4. **Solve for $y$:** Divide both sides by $58.5$: $$y = \frac{9.7 - 85x}{58.5}$$ 5. **Simplify the fraction:** This is the simplest form expressing $y$ in terms of $x$. 6. **Interpretation:** For any value of $x$, you can find $y$ using this formula. This represents a straight line in the $xy$-plane.