find equation of a line perpendicular to the given line through the given point

Question

Find equation of a line perpendicular to the given line through the given point:
The line is $y=\frac{1}{2}x-2$
The point is $(3,6)$

I don't know what to do or try, please help me, its probably very easy to other people

Answer 1

Slope of given line is : $m_1 = \frac{1}{2}$

If two lines are perpendicular, then the product of their slopes is $-1$. Exception being the lines are $x$ and $y$ axes which is not the case here. hence:

$$m_1*m_2 = -1$$ $$\frac{1}{2} * m_2 = -1$$ $$ m_2 = -2$$ Now calculate the line equation of line with slope = $-2$ and passing through point $(3,6)$. $$(y-6) = -2(x-3)$$ $$2x + y = 12$$ $$ y = -2x + 12$$