1. The problem involves finding the equation of a line given points and verifying or using linear functions. 2. For a linear function, the general form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. To find the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$, use the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 4. Using the points $(3, 3)$ and $(8, 13)$: $$m = \frac{13 - 3}{8 - 3} = \frac{10}{5} = 2$$ 5. Now use point-slope form to find $b$: $$y = mx + b \Rightarrow 3 = 2 \times 3 + b \Rightarrow 3 = 6 + b$$ 6. Solve for $b$: $$b = 3 - 6 = -3$$ 7. The equation of the line is: $$y = 2x - 3$$ 8. Check the function with $x=5$: $$y = 2 \times 5 - 3 = 10 - 3 = 7$$ 9. This matches the pattern given in the problem. Final answer: $$y = 2x - 3$$