1. **State the problem:** Find the equation of the line passing through the point $(6, -5)$ with slope $m = -\frac{1}{3}$. 2. **Formula used:** The point-slope form of a line is given by: $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope. 3. **Substitute the given values:** $$y - (-5) = -\frac{1}{3}(x - 6)$$ which simplifies to $$y + 5 = -\frac{1}{3}x + 2$$ 4. **Isolate $y$ to get slope-intercept form:** $$y = -\frac{1}{3}x + 2 - 5$$ $$y = -\frac{1}{3}x - 3$$ 5. **Final answer:** The equation of the line is $$y = -\frac{1}{3}x - 3$$ This means the line decreases by $\frac{1}{3}$ unit vertically for every 1 unit increase horizontally and passes through the point $(6, -5)$.