1. **State the problem:** Find the equation of the line passing through the points $(2,8)$ and $(5,-6)$.\n\n2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}.$$\n\n3. **Calculate the slope:** Substitute the points $(2,8)$ and $(5,-6)$:\n$$m=\frac{-6 - 8}{5 - 2} = \frac{-14}{3}.$$\n\n4. **Use point-slope form:** The equation of the line is $$y - y_1 = m(x - x_1).$$ Using point $(2,8)$:\n$$y - 8 = -\frac{14}{3}(x - 2).$$\n\n5. **Simplify the equation:**\n$$y - 8 = -\frac{14}{3}x + \frac{28}{3}$$\n$$y = -\frac{14}{3}x + \frac{28}{3} + 8$$\n$$y = -\frac{14}{3}x + \frac{28}{3} + \frac{24}{3}$$\n$$y = -\frac{14}{3}x + \frac{52}{3}.$$\n\n6. **Final answer:** The equation of the line is $$y = -\frac{14}{3}x + \frac{52}{3}.$$