1. **State the problem:** Solve the inequality $x + 3y \ge 9$ for $y$ in terms of $x$. 2. **Isolate $y$:** To express $y$ in terms of $x$, subtract $x$ from both sides: $$x + 3y \ge 9 \implies 3y \ge 9 - x$$ 3. **Divide both sides by 3:** Since 3 is positive, the inequality direction remains the same: $$\cancel{3}y \ge \frac{9 - x}{\cancel{3}} \implies y \ge 3 - \frac{x}{3}$$ 4. **Interpretation:** The solution set includes all points $(x,y)$ where $y$ is greater than or equal to $3 - \frac{x}{3}$. 5. **Summary:** The inequality $x + 3y \ge 9$ is equivalent to $$y \ge 3 - \frac{x}{3}$$ which describes a half-plane above the line $y = 3 - \frac{x}{3}$ including the line itself.