Line Equations F0F2Df

1. **State the problem:** We need to find the equation of line $L$ that passes through the point $(-4, -4)$ and is parallel to the line $y = 5x$. 2. **Recall the slope of the given line:** The line $y = 5x$ is in slope-intercept form $y = mx + b$, where $m$ is the slope. Here, $m = 5$. 3. **Parallel lines have the same slope:** Since $L$ is parallel to $y = 5x$, the slope of $L$ is also $5$. 4. **Use point-slope form:** 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. Substitute $m = 5$ and point $(-4, -4)$: $$y - (-4) = 5(x - (-4))$$ which simplifies to $$y + 4 = 5(x + 4)$$ 5. **Convert to slope-intercept form:** Expand and simplify: $$y + 4 = 5x + 20$$ Subtract $4$ from both sides: $$y = 5x + 20 - 4$$ $$y = 5x + 16$$ 6. **Final answers:** - Point-slope form: $$y + 4 = 5(x + 4)$$ - Slope-intercept form: $$y = 5x + 16$$