Parallel Line A4Bc27

1. **State the problem:** We need to find the equation of a line parallel to $y=-3x+1$ that passes through the point $(-2,-4)$. 2. **Recall the formula:** Lines that are parallel have the same slope. The slope-intercept form of a line is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Identify the slope:** From the given line $y=-3x+1$, the slope is $m=-3$. 4. **Use the point-slope form:** The equation of a line with slope $m$ passing through point $(x_1,y_1)$ is $$y-y_1=m(x-x_1)$$. Substitute $m=-3$, $x_1=-2$, and $y_1=-4$: $$y-(-4)=-3(x-(-2))$$ which simplifies to $$y+4=-3(x+2)$$ 5. **Distribute and simplify:** $$y+4=-3x-6$$ 6. **Isolate $y$ to get slope-intercept form:** $$y=-3x-6-4$$ $$y=-3x-10$$ 7. **Final answer:** The equation of the line parallel to $y=-3x+1$ passing through $(-2,-4)$ is $$y=-3x-10$$