Question

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

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. 1
• D. $\frac{4}{3}$

Answer 1

The correct option is D

$\frac{4}{3}$

The equation of the line perpendicular to $3x+y=3$ is given below :

$x-3y+\lambda =0$

This line passes through $(2,2)$

$2-6+\lambda =0$

$\Rightarrow \lambda =4$

So, the equation of the line will be

$x-3y+4=0$

$\Rightarrow y=\frac{1}{3}x+\frac{4}{3}$

Hence, the y-intercept is $\frac{4}{3}.$