Question

A line is perpendicular to $3x+y=3$ and passes through a point $(2,2).$ Its $y$ intercept is

• A. $2/3$
• B. $1/3$
• C. $1$
• D. $4/3$

Answer 1

The correct option is D $4/3$

Slope of line $3x+y=3$ is $m=-3$
Hence slope of perpendicular line is $m^{\prime }=\frac{1}{3}$
Therefore equation of perpendicular line is
$(y-2)=\frac{1}{3}(x-2)\Rightarrow 3y-6=x-2\Rightarrow x-3y+4=0$
So y-intercept is $y=\frac{4}{3}.$