1. **State the problem:** We need to find the y-intercept of the straight line passing through the points $(2, 15)$ and $(6, 39)$. 2. **Formula used:** The equation of a line in slope-intercept form is $$y = mx + c$$ where $m$ is the slope and $c$ is the y-intercept. 3. **Calculate the slope $m$:** The slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Substitute the points: $$m = \frac{39 - 15}{6 - 2} = \frac{24}{4} = 6$$ 4. **Find the y-intercept $c$:** Use the slope and one point to solve for $c$. Using point $(2, 15)$: $$15 = 6 \times 2 + c$$ $$15 = 12 + c$$ $$c = 15 - 12 = 3$$ 5. **Final answer:** The y-intercept of the line is $3$.