1. **State the problem:** Given the table of values for $x$ and $y$, find the relationship or function that connects $x$ and $y$. 2. **Observe the data:** The table shows: $$\begin{array}{c|c} x & y \\\hline 0 & 1 \\ 1 & 2 \\ 2 & 3 \\ 3 & 4 \\ 4 & 5 \\ \end{array}$$ 3. **Look for a pattern:** Notice that as $x$ increases by 1, $y$ also increases by 1. 4. **Formulate the function:** This suggests a linear relationship of the form: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 5. **Calculate the slope $m$:** Using two points, for example $(0,1)$ and $(1,2)$: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 1}{1 - 0} = 1$$ 6. **Find the y-intercept $b$:** Since when $x=0$, $y=1$, then: $$b = 1$$ 7. **Write the final function:** $$y = 1 \cdot x + 1 = x + 1$$ **Answer:** The function that relates $x$ and $y$ is $y = x + 1$.