1. **State the problem:** Find the equation of the line passing through the points $(-3, -1)$ and $(8, -6)$.\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:**\n$$m = \frac{-6 - (-1)}{8 - (-3)} = \frac{-6 + 1}{8 + 3} = \frac{-5}{11}.$$\n\n4. **Use point-slope form:** The equation of the line is $$y - y_1 = m(x - x_1).$$\nUsing point $(-3, -1)$, we get\n$$y - (-1) = -\frac{5}{11}(x - (-3))$$\nwhich simplifies to\n$$y + 1 = -\frac{5}{11}(x + 3).$$\n\n5. **Distribute the slope:**\n$$y + 1 = -\frac{5}{11}x - \frac{15}{11}.$$\n\n6. **Isolate $y$ to get slope-intercept form:**\n$$y = -\frac{5}{11}x - \frac{15}{11} - 1.$$\n\n7. **Simplify the constant term:**\n$$y = -\frac{5}{11}x - \frac{15}{11} - \frac{11}{11} = -\frac{5}{11}x - \frac{26}{11}.$$\n\n**Final answer:** The equation of the line is $$y = -\frac{5}{11}x - \frac{26}{11}.$$