1. **State the problem:** We are given a point $(2, -9)$ and a slope $m = 3$. We need to find the equation of the line in slope-intercept form $y = mx + b$ that passes through this point. 2. **Formula used:** The point-slope form of a line is $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope. 3. **Substitute the known values:** $$y - (-9) = 3(x - 2)$$ which simplifies to $$y + 9 = 3x - 6$$ 4. **Isolate $y$ to get slope-intercept form:** $$y = 3x - 6 - 9$$ $$y = 3x - 15$$ 5. **Interpretation:** The equation of the line with slope 3 passing through $(2, -9)$ is $$y = 3x - 15$$ 6. **Check options:** Among the given options, the correct one is $$y = 3x - 15$$ Final answer: $$y = 3x - 15$$