1. **State the problem:** We are given the equation $y = x + 6$ and a table of values for $x$ and $y$: $$\begin{array}{c|cccccc} x & 2 & 3 & 4 & 5 & 9 & 10 \\ y & -6 & -9 & -12 & -15 & -27 & -30 \\ \end{array}$$ We want to check if the slope of the equation matches the slope calculated from the table values. 2. **Recall the slope formula:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope of the equation $y = x + 6$:** The equation is in slope-intercept form $y = mx + b$ where $m$ is the slope. Here, $m = 1$. 4. **Calculate the slope from the table values:** Choose two points from the table, for example $(2, -6)$ and $(3, -9)$. Calculate: $$m = \frac{-9 - (-6)}{3 - 2} = \frac{-9 + 6}{1} = \frac{-3}{1} = -3$$ 5. **Check the slope consistency:** The slope from the equation is $1$, but the slope from the table is $-3$. Therefore, the slopes are not the same. 6. **Conclusion:** The table values do not correspond to the equation $y = x + 6$ because their slopes differ. **Final answer:** The slopes are not the same.