1. **State the problem:** Find the equation of the line passing through the points $(3,-8)$ and $(6,-4)$. 2. **Formula used:** 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:** $$m=\frac{-4 - (-8)}{6 - 3} = \frac{-4 + 8}{3} = \frac{4}{3}$$ 4. **Use point-slope form:** The equation of the line is $$y - y_1 = m(x - x_1)$$ Using point $(3,-8)$, $$y - (-8) = \frac{4}{3}(x - 3)$$ 5. **Simplify:** $$y + 8 = \frac{4}{3}x - \frac{4}{3} \times 3$$ $$y + 8 = \frac{4}{3}x - 4$$ 6. **Isolate $y$:** $$y = \frac{4}{3}x - 4 - 8$$ $$y = \frac{4}{3}x - 12$$ **Final answer:** The equation of the line is $$y = \frac{4}{3}x - 12$$