1. **State the problem:** Solve the linear equation $$6x + 9y - 12 = 0$$ for $y$ in terms of $x$. 2. **Rewrite the equation:** The goal is to isolate $y$. Start by moving all terms except those with $y$ to the other side: $$6x + 9y - 12 = 0 \implies 9y = 12 - 6x$$ 3. **Divide both sides by 9:** To solve for $y$, divide each term by 9: $$y = \frac{12 - 6x}{9}$$ 4. **Simplify the fraction:** Factor numerator and denominator if possible: $$y = \frac{6(2 - x)}{9} = \frac{6}{9}(2 - x) = \frac{2}{3}(2 - x)$$ 5. **Distribute the fraction:** $$y = \frac{2}{3} \times 2 - \frac{2}{3} \times x = \frac{4}{3} - \frac{2}{3}x$$ **Final answer:** $$y = \frac{4}{3} - \frac{2}{3}x$$ This expresses $y$ as a function of $x$ for the given linear equation.