1. **State the problem:** Find the equation and y-intercept of the line passing through points (2, -4) and (6, 8). 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:** $$m=\frac{8 - (-4)}{6 - 2}=\frac{8 + 4}{4}=\frac{12}{4}=3$$ 4. **Use point-slope form:** The equation of a line with slope $m$ passing through $(x_1,y_1)$ is $$y - y_1 = m(x - x_1)$$ Using point $(2,-4)$: $$y - (-4) = 3(x - 2)$$ $$y + 4 = 3x - 6$$ 5. **Simplify to slope-intercept form:** $$y = 3x - 6 - 4$$ $$y = 3x - 10$$ 6. **Identify y-intercept:** The y-intercept is the value of $y$ when $x=0$: $$y = 3(0) - 10 = -10$$ So the y-intercept is $-10$. **Final answer:** The equation of the line is $$y = 3x - 10$$ and the y-intercept is $-10$.