1. **State the problem:** Find the equation of the line passing through the point $P(-1, 2)$ with slope $m = -\frac{5}{1} = -5$. 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 known values:** $$y - 2 = -5(x - (-1))$$ which simplifies to $$y - 2 = -5(x + 1)$$ 4. **Distribute the slope:** $$y - 2 = -5x - 5$$ 5. **Isolate $y$ to get slope-intercept form:** $$y = -5x - 5 + 2$$ 6. **Simplify the constants:** $$y = -5x - 3$$ **Final answer:** The equation of the line is $$y = -5x - 3$$