1. **State the problem:** We need to find the y-intercept of the straight line passing through the points $(2, 13)$ and $(8, 37)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope:** $$m = \frac{37 - 13}{8 - 2} = \frac{24}{6} = 4$$ 4. **Equation of the line:** Using point-slope form: $$y - y_1 = m(x - x_1)$$ Substitute $m=4$ and point $(2, 13)$: $$y - 13 = 4(x - 2)$$ 5. **Simplify to slope-intercept form $y = mx + c$:** $$y - 13 = 4x - 8$$ $$y = 4x - 8 + 13$$ $$y = 4x + 5$$ 6. **Identify the y-intercept:** The y-intercept $c$ is the constant term when $x=0$: $$c = 5$$ **Final answer:** The y-intercept of the line is $5$.