Question

Parallel to the y=-3x through the point (-1,2)

Answer 1

`\huge\boxed{y=-3x-1}`

Explanation:

`\text{Let}\ k:y=m_1x+b_1;\ l:y=m_2x+b_2.\\\\l\ ||\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\\text{We have}\ y=-3x\to m_1=-3.\\\\\text{Therefore, we have a initial parallel line equation:}\\\\y=-3x+b\\\\\text{The line passes trough the point}\ (-1,\ 2).\\\\\text{Substitute}\ x=-1,\ y=2:\\\\2=-3(-1)+b\\2=3+b\qquad\text{subtract 3 from both sides}\\-1=b\to b=-1\\\\\text{Finally:}\\\\y=-3x-1`