1. **State the problem:** We are given a table of values for $x$ and $y$ and need to find the equation that represents the relationship between $x$ and $y$. 2. **Given table:** $$\begin{array}{c|c} x & y \\\hline -2 & -1 \\ -1 & 1 \\ 0 & 3 \\ 1 & 5 \\ 2 & 7 \end{array}$$ 3. **Identify the type of relationship:** The problem states it is linear, so the equation is of the form: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 4. **Calculate the slope $m$:** The slope formula is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(0,3)$ and $(1,5)$: $$m = \frac{5 - 3}{1 - 0} = \frac{2}{1} = 2$$ 5. **Find the y-intercept $b$:** Use the point $(0,3)$ where $x=0$, so $y=b$: $$b = 3$$ 6. **Write the equation:** $$y = 2x + 3$$ 7. **Verify with other points:** For $x = -2$: $$y = 2(-2) + 3 = -4 + 3 = -1$$ Matches the table. 8. **Conclusion:** The equation representing the relationship is: $$\boxed{y = 2x + 3}$$ This corresponds to option D.