Question

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

Answer 1

`\large\boxed{y=(2)/(3)x+7}`

Explanation:

`\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=-(1)/(m_1)\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\y=-(3)/(2)x+4\to m_1=-(3)/(2)\\\\m_2=-(1)/(m_1)\Rightarrow m_2=-(1)/(-(3)/(2))=(2)/(3)\\\\\text{Therefore we have the equation:}\ y=(2)/(3)x+b.\\\\\text{Put the coordinates of the point (3, 9) to the equation:}\\\\9=(2)/(3)(3)+b\\\\9=2+b\qquad\text{subtract 2 from both sides}\\\\7=b\to b=7`