Question

Which of the following is the equation of s line perpendicular to the line y=-3/2x+4, passing through the point (3,9)

Answer 1

`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=-(3)/(2)x+4\to m_1=-(3)/(2)\\\\m_1m_2=-1\to-(3)/(2)m_2=-1\ \ \ |\cdot\left(-(2)/(3)\right)\\\\m_2=(2)/(3)\\\\l:y=m_2x+b\to y=(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=(2)/(3)\cdot3+b\\\\9=2+b\ \ \ \ |-2\\\\b=7\\\\Answer:\ l:\boxed{y=(2)/(3)x+7}`