Line Equation D8B925

1. **State the problem:** We need to find the equation of line L which crosses the y-axis at $3$ and passes through the point $(1, -1)$. 2. **Recall the slope-intercept form:** The equation of a line can be written as $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Identify the y-intercept:** From the problem, the line crosses the y-axis at $3$, so $$b = 3$$. 4. **Calculate the slope $m$:** The slope is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$. Using points $(0, 3)$ (y-intercept) and $(1, -1)$: $$m = \frac{-1 - 3}{1 - 0} = \frac{-4}{1} = -4$$. 5. **Write the equation:** Substitute $m = -4$ and $b = 3$ into the slope-intercept form: $$y = -4x + 3$$. 6. **Final answer:** The equation of line L is $$\boxed{y = -4x + 3}$$.