1. **State the problem:** Solve the linear equation $5x + 9y = 45$ for $y$ in terms of $x$. 2. **Formula and rules:** To express $y$ as a function of $x$, isolate $y$ on one side of the equation. 3. **Isolate $y$:** $$5x + 9y = 45$$ Subtract $5x$ from both sides: $$\cancel{5x} + 9y - \cancel{5x} = 45 - 5x$$ which simplifies to $$9y = 45 - 5x$$ 4. **Solve for $y$ by dividing both sides by 9:** $$y = \frac{45 - 5x}{9}$$ Show cancellation: $$y = \frac{\cancel{45} - 5x}{\cancel{9}}$$ Since 45 and 9 share a factor of 9, simplify: $$y = 5 - \frac{5}{9}x$$ 5. **Final answer:** $$y = 5 - \frac{5}{9}x$$ This expresses $y$ as a function of $x$ for the given linear equation.