1. **State the problem:** Solve the linear equation $2x + 4y = 9$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by moving other terms to the opposite side and then dividing by the coefficient of $y$. 3. **Isolate $y$:** $$2x + 4y = 9$$ Subtract $2x$ from both sides: $$\cancel{2x} + 4y - \cancel{2x} = 9 - 2x$$ which simplifies to $$4y = 9 - 2x$$ 4. **Divide both sides by 4 to solve for $y$:** $$y = \frac{9 - 2x}{4}$$ Show the cancellation: $$y = \frac{\cancel{4} \cdot \frac{9 - 2x}{4}}{\cancel{4}}$$ 5. **Final answer:** $$y = \frac{9}{4} - \frac{2}{4}x = \frac{9}{4} - \frac{1}{2}x$$ This expresses $y$ in terms of $x$. You can also write the function as: $$y = -\frac{1}{2}x + \frac{9}{4}$$