1. **State the problem:** Complete the table for the equation $x + 12 = 6y$ and verify the points. 2. **Rewrite the equation in slope-intercept form:** $$x + 12 = 6y$$ Divide both sides by 6 to solve for $y$: $$y = \frac{x + 12}{6}$$ Show canceling common factors if any: $$y = \frac{\cancel{6}x + \cancel{12}}{\cancel{6}}$$ Actually, 12 is not divisible by 6 in the numerator as a term, so rewrite as: $$y = \frac{x}{6} + 2$$ 3. **Use the formula $y = \frac{x}{6} + 2$ to find $y$ for each $x$ in the table:** - For $x = -12$: $$y = \frac{-12}{6} + 2 = -2 + 2 = 0$$ - For $x = -6$: $$y = \frac{-6}{6} + 2 = -1 + 2 = 1$$ - For $x = 0$: $$y = \frac{0}{6} + 2 = 0 + 2 = 2$$ - For $x = 6$: $$y = \frac{6}{6} + 2 = 1 + 2 = 3$$ - For $x = 12$: $$y = \frac{12}{6} + 2 = 2 + 2 = 4$$ 4. **Compare with the given table:** Given $y$ values are $-2, -1, 2, 3, 4$ for $x = -12, -6, 0, 6, 12$ respectively. Our calculated $y$ values are $0, 1, 2, 3, 4$. There is a discrepancy for $x = -12$ and $x = -6$ in the given table. 5. **Conclusion:** The correct $y$ values for the given $x$ values using the equation $x + 12 = 6y$ are: | $x$ | $y$ | |-----|-----| | -12 | 0 | | -6 | 1 | | 0 | 2 | | 6 | 3 | | 12 | 4 | The points $(-12, -2)$ and $(-6, -1)$ do not satisfy the equation. **Final answer:** The correct points on the line $x + 12 = 6y$ are $(-12,0), (-6,1), (0,2), (6,3), (12,4)$.