Question

Find the equation of the line that is perpendicular to the given line and passes through the given point. Enter the right side of the equation as as a single fraction. y=3x-12/2; (9,9)

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-12)/(2)=(3x)/(2)-(12)/(2)=(3)/(2)x-6\to m_1=(3)/(2)\\\\l:y=mx+b\to(3)/(2)m=-1\qquad|\cdot(2)/(3)\\\\m=-(2)/(3)\\\\l:y=-(2)/(3)x+b\\\\\text{Put the coordinates of the point (9, 9) to the equation of the line}\ l:\\\\9=-(2)/(3)(9)+b\\\\9=-2(9)+b\\\\9=-18+b\qquad|+18\\\\b=27\\\\y=-(2)/(3)x+27\to y=-(2x)/(3)+(27\cdot3)/(3)\to\boxed{y=(-2x+81)/(3)}`