1. **State the problem:** We are given the equation $x + 12 = 6y$ and need to complete the table of values for $x$ and $y$. 2. **Rewrite the equation to solve for $y$:** $$x + 12 = 6y$$ Divide both sides by 6: $$\frac{x + 12}{6} = y$$ Using cancellation notation: $$y = \frac{\cancel{x} + 12}{\cancel{6}}$$ This means for each $x$, $y = \frac{x + 12}{6}$. 3. **Calculate $y$ for each $x$ value:** - For $x = -12$: $y = \frac{-12 + 12}{6} = \frac{0}{6} = 0$ - For $x = -6$: $y = \frac{-6 + 12}{6} = \frac{6}{6} = 1$ - For $x = 0$: $y = \frac{0 + 12}{6} = \frac{12}{6} = 2$ - For $x = 6$: $y = \frac{6 + 12}{6} = \frac{18}{6} = 3$ - For $x = 12$: $y = \frac{12 + 12}{6} = \frac{24}{6} = 4$ 4. **Complete the table:** | $x$ | $y$ | |-----|-----| | -12 | 0 | | -6 | 1 | | 0 | 2 | | 6 | 3 | | 12 | 4 | 5. **Explanation:** To find $y$, we isolate it by dividing the entire equation by 6. Then, for each $x$ value, substitute it into the formula $y = \frac{x + 12}{6}$ and simplify. This method helps you fill in the table and plot the points on the graph easily. **Final answer:** | $x$ | $y$ | |-----|-----| | -12 | 0 | | -6 | 1 | | 0 | 2 | | 6 | 3 | | 12 | 4 |