[tex]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=-\dfrac{3}{2}x+4\to m_1=-\dfrac{3}{2}\\\\m_1m_2=-1\to-\dfrac{3}{2}m_2=-1\ \ \ |\cdot\left(-\dfrac{2}{3}\right)\\\\m_2=\dfrac{2}{3}\\\\l:y=m_2x+b\to y=\dfrac{2}{3}x+b\\\\\text{The line l passing throught the point}\ (3,\ 9).\\\\\text{Put the values of coordinates of the point to the equation of the line l}\\\\9=\dfrac{2}{3}\cdot3+b\\\\9=2+b\ \ \ \ |-2\\\\b=7\\\\Answer:\ l:\boxed{y=\dfrac{2}{3}x+7}[/tex]
