1. **State the problem:** We need to find the equation of the line passing through the points $(-1,0)$ and $(0,-4)$. 2. **Formula used:** The equation of a line can be found using the slope-intercept form: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(-1,0)$ and $(0,-4)$, $$m = \frac{-4 - 0}{0 - (-1)} = \frac{-4}{1} = -4$$ 4. **Find the y-intercept $b$:** Since the point $(0,-4)$ lies on the line, the y-intercept is $b = -4$. 5. **Write the equation:** Substitute $m = -4$ and $b = -4$ into the slope-intercept form: $$y = -4x - 4$$ 6. **Final answer:** The equation of the line is $$y = -4x - 4$$