[tex]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=-\dfrac{1}{3}\\\\l:y=-\dfrac{1}{3}x+b\\\\\text{Put the coordinates of the point (3, 1) to the equation of the line}\ l:\\\\1=-\dfrac{1}{3}(3)+b\\\\1=-1+b\qquad|+1\\\\b=2\\\\Answer:\ y=-\dfrac{1}{3}x+2[/tex]
