Question

A line passes through the origin and has a slope of –3. What is the equation of the line that is perpendicular to the first line and passes through the point (3, 4)?

Answer 1

The given line has slope $m=-3$. The slope of the line perpendicular to this line is $-\frac{1}{m} =\frac{1}{3}$.

Its equation is $y=\frac{1}{3} x+c$. Since this line passes through, $(3,4)$,

$4=\frac{1}{3} (3)+c\\ c=3$

Thus the equation of the line in slope intercept form is $y=\frac{1}{3} x+3$