1. **State the problem:** Find the equation of the line passing through the point $(0,-1)$ with slope $m=3$. 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:** $$y - (-1) = 3(x - 0)$$ which simplifies to $$y + 1 = 3x$$ 4. **Solve for $y$ to get slope-intercept form:** $$y = 3x - 1$$ 5. **Explanation:** We used the point-slope formula to write the equation of the line. Since the point is $(0,-1)$, the $y$-intercept is directly $-1$. The slope $3$ tells us the line rises 3 units vertically for every 1 unit it moves horizontally. **Final answer:** $$y = 3x - 1$$