1. **State the problem:** We are given a line passing through points $(-7, -8)$ and $(1, 6)$ and asked to find the y-intercept of this line. 2. **Formula and rules:** The y-intercept is the point where the line crosses the y-axis, which means $x=0$. To find it, we first find the slope $m$ of the line using the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope:** $$m = \frac{6 - (-8)}{1 - (-7)} = \frac{6 + 8}{1 + 7} = \frac{14}{8}$$ 4. **Simplify the slope:** $$m = \frac{\cancel{14}}{\cancel{8}} = \frac{7}{4}$$ 5. **Use point-slope form to find the equation:** Using point $(1,6)$: $$y - 6 = \frac{7}{4}(x - 1)$$ 6. **Simplify to slope-intercept form $y=mx+b$:** $$y - 6 = \frac{7}{4}x - \frac{7}{4}$$ $$y = \frac{7}{4}x - \frac{7}{4} + 6$$ 7. **Combine constants:** $$6 = \frac{24}{4}$$ $$y = \frac{7}{4}x + \left(-\frac{7}{4} + \frac{24}{4}\right) = \frac{7}{4}x + \frac{17}{4}$$ 8. **Find the y-intercept:** The y-intercept is the constant term $b = \frac{17}{4} = 4.25$. **Note:** The problem states the y-intercept is 2, but based on the points given, the calculated y-intercept is $\frac{17}{4}$. **Final answer:** The y-intercept of the line is $\boxed{\frac{17}{4}}$ or 4.25.