1. **State the problem:** Solve the linear equation $$x + 3y = 15$$ for $y$ in terms of $x$ and create a table and graph. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation. This involves subtracting $x$ from both sides and then dividing by 3. 3. **Isolate $y$:** $$x + 3y = 15$$ Subtract $x$ from both sides: $$\cancel{x} + 3y - \cancel{x} = 15 - x$$ $$3y = 15 - x$$ 4. **Divide both sides by 3:** $$\frac{3y}{\cancel{3}} = \frac{15 - x}{3}$$ $$y = \frac{15 - x}{3}$$ 5. **Create a table of values:** Choose values for $x$ and calculate corresponding $y$ values. | $x$ | $y = \frac{15 - x}{3}$ | |-----|-----------------------| | 0 | $\frac{15 - 0}{3} = 5$ | | 3 | $\frac{15 - 3}{3} = 4$ | | 6 | $\frac{15 - 6}{3} = 3$ | | 9 | $\frac{15 - 9}{3} = 2$ | | 12 | $\frac{15 - 12}{3} = 1$ | 6. **Graph:** The graph is a straight line with intercepts at $x=15$ when $y=0$ and $y=5$ when $x=0$. **Final answer:** $$y = \frac{15 - x}{3}$$