1. **State the problem:** Determine if the given table of values satisfies a linear equation. 2. **Recall the formula for a linear equation:** A linear equation in two variables $x$ and $y$ can be written as $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$ using two points from the table:** Using points $(0, -4)$ and $(1, -1)$, $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - (-4)}{1 - 0} = \frac{3}{1} = 3$$ 4. **Check if the slope is consistent for other points:** Between $(1, -1)$ and $(2, 2)$: $$m = \frac{2 - (-1)}{2 - 1} = \frac{3}{1} = 3$$ Between $(2, 2)$ and $(3, 5)$: $$m = \frac{5 - 2}{3 - 2} = \frac{3}{1} = 3$$ Between $(3, 5)$ and $(4, 8)$: $$m = \frac{8 - 5}{4 - 3} = \frac{3}{1} = 3$$ Between $(4, 8)$ and $(5, 11)$: $$m = \frac{11 - 8}{5 - 4} = \frac{3}{1} = 3$$ All slopes are equal to 3, confirming a constant rate of change. 5. **Find the y-intercept $b$ using point $(0, -4)$:** $$y = mx + b \Rightarrow -4 = 3 \times 0 + b \Rightarrow b = -4$$ 6. **Write the linear equation:** $$y = 3x - 4$$ 7. **Verify the equation with another point, e.g., $(5, 11)$:** $$y = 3(5) - 4 = 15 - 4 = 11$$ which matches the table. **Conclusion:** The table satisfies the linear equation $$y = 3x - 4$$.