1. **State the problem:** Find the equation of the line passing through the point $(-1, -1)$ with slope $\frac{9}{2}$. 2. **Formula used:** The point-slope form of a line is given by $$y - y_1 = m(x - x_1)$$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line. 3. **Substitute the given values:** Here, $m = \frac{9}{2}$, $x_1 = -1$, and $y_1 = -1$. $$y - (-1) = \frac{9}{2}(x - (-1))$$ 4. **Simplify the signs:** $$y + 1 = \frac{9}{2}(x + 1)$$ This is the equation of the line in point-slope form, as requested. **Final answer:** $$y + 1 = \frac{9}{2}(x + 1)$$