Question

What is an equation of the line that is perpendicular to y=3x−9 and that passes through the point (3, 1) ?

Answer 1

`Let\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\\\\\text{We have}\ k:y=3x-9\to m_1=3\\\\l:y=mx+b\to3m=-1\qquad|:3\\\\m=-(1)/(3)\\\\l:y=-(1)/(3)x+b\\\\\text{Put the coordinates of the point (3, 1) to the equation of the line}\ l:\\\\1=-(1)/(3)(3)+b\\\\1=-1+b\qquad|+1\\\\b=2\\\\Answer:\ y=-(1)/(3)x+2`