1. **State the problem:** Solve the linear equation $x + 3y = 15$ for $y$ and understand its graph. 2. **Formula and rules:** To graph a linear equation, it's often easiest to solve for $y$ in terms of $x$. The equation is in the form $Ax + By = C$, so solve for $y$: $$x + 3y = 15$$ 3. **Isolate $y$:** $$3y = 15 - x$$ 4. **Divide both sides by 3:** $$y = \frac{15 - x}{3}$$ Show cancelation: $$y = \frac{\cancel{15} - x}{\cancel{3}}$$ Actually, 15 and 3 don't cancel directly, so keep as: $$y = 5 - \frac{x}{3}$$ 5. **Interpretation:** This means for any $x$, $y$ equals $5 - \frac{x}{3}$. 6. **Create a table of values:** Choose values for $x$ and compute $y$. | $x$ | $y = 5 - \frac{x}{3}$ | |-----|-----------------------| | 0 | $5 - 0 = 5$ | | 3 | $5 - 1 = 4$ | | 6 | $5 - 2 = 3$ | | 9 | $5 - 3 = 2$ | | 15 | $5 - 5 = 0$ | 7. **Graph:** The line crosses the $y$-axis at $(0,5)$ and the $x$-axis at $(15,0)$. **Final answer:** The equation solved for $y$ is $$y = 5 - \frac{x}{3}$$ and the table above shows points on the line.