1. **State the problem:** Given the table of values where $x = 1, 2, 3, 4, 5$ and corresponding $y = 33, 34, 35, 36, 37$, find the linear equation that relates $y$ to $x$. 2. **Identify the relationship:** The table shows that as $x$ increases by 1, $y$ increases by 1. This suggests a linear function of the form: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** The slope is the change in $y$ divided by the change in $x$: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{34 - 33}{2 - 1} = \frac{1}{1} = 1$$ 4. **Find the y-intercept $b$:** Use one point from the table, for example $(x, y) = (1, 33)$, and substitute into the equation $y = mx + b$: $$33 = 1 \times 1 + b$$ $$33 = 1 + b$$ Subtract 1 from both sides: $$33 - 1 = b$$ $$b = 32$$ 5. **Write the final equation:** $$y = 1 \times x + 32$$ or simply $$y = x + 32$$ This equation models the linear relationship between $x$ and $y$ in the table.