Question

Write an equation of the line that is perpendicular to the line y =

1
3
x + 6 that passes through the point (2,-3).

Answer 1

y = -3x + 3

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\\\\===============================`

`\text{We have the equation}\ y=(1)/(3)x+6\to m_1=(1)/(3).\\\\\text{Therefore}\ m_2=-(1)/((1)/(3))=-3.\\\\\text{We have the equation}\ y=-3x+b.\\\\\text{Put the coordinates of the point}\ (2,\ -3):\\\\-3=-3(2)+b\\-3=-6+b\qquad\text{add 6 to both sides}\\3=b\to b=3\\\\\text{Finally:}\\\\y=-3x+3`