1. **State the problem:** We need to find the point-slope form of a line with slope $m = -\frac{3}{4}$ passing through the point $(2, -5)$. 2. **Recall the point-slope form formula:** $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope. 3. **Substitute the given values:** $$y - (-5) = -\frac{3}{4}(x - 2)$$ which simplifies to $$y + 5 = -\frac{3}{4}(x - 2)$$ 4. **This is the point-slope form of the line:** $$\boxed{y + 5 = -\frac{3}{4}(x - 2)}$$ This equation represents the line with slope $-\frac{3}{4}$ passing through $(2, -5)$.