1. **State the problem:** We have a table of values for $x$ and $y$: | $x$ | 1 | 2 | 3 | 4 | 5 | |-----|---|---|---|---|---| | $y$ | 3 | 5 | 8 | 11 | 13 | We want to find the equation of the line of best fit (linear regression) from the given options: - $y = 2.6x + 0.1$ - $y = 2.6x + 0.4$ - $y = 2.6x + 0.2$ - $y = 0.2x + 2.6$ - $y = 0.2x + 2.8$ 2. **Formula for linear regression line:** The line of best fit has the form: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** The slope formula is: $$m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(1,3)$ and $(5,13)$: $$m = \frac{13 - 3}{5 - 1} = \frac{10}{4} = 2.5$$ 4. **Calculate the y-intercept $b$:** Use the point-slope form with point $(1,3)$: $$3 = 2.5 \times 1 + b$$ $$b = 3 - 2.5 = 0.5$$ 5. **Equation of the line:** $$y = 2.5x + 0.5$$ 6. **Compare with given options:** None of the options exactly match $y = 2.5x + 0.5$, but the closest slope is $2.6$ and intercept near $0.2$ or $0.1$. 7. **Check values for $y = 2.6x + 0.2$:** At $x=1$, $y=2.6(1)+0.2=2.8$ (close to 3) At $x=5$, $y=2.6(5)+0.2=13.2$ (close to 13) This fits better than others. **Final answer:** $$\boxed{y = 2.6x + 0.2}$$