Answer:
[tex]\large\boxed{y=\dfrac{2}{3}x+7}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\y=-\dfrac{3}{2}x+4\to m_1=-\dfrac{3}{2}\\\\m_2=-\dfrac{1}{m_1}\Rightarrow m_2=-\dfrac{1}{-\frac{3}{2}}=\dfrac{2}{3}\\\\\text{Therefore we have the equation:}\ y=\dfrac{2}{3}x+b.\\\\\text{Put the coordinates of the point (3, 9) to the equation:}\\\\9=\dfrac{2}{3}(3)+b\\\\9=2+b\qquad\text{subtract 2 from both sides}\\\\7=b\to b=7[/tex]
