Question

A line passes through $(2,2)$ and is perpendicular to the line $3x+y=3$ its $y$ intercepts is :

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

Answer 1

The correct option is D $\frac{4}{3}$

Equation of line perpendicular to $3x+y=3$ is $x-3y=c$......(1).

Given the line (1) passes through $(2,2)$, then,

$2-6=c$

or, $c=-4$.

Then the equation of the line is

$x-3y=-4$

or, $\frac{x}{-4}+\frac{y}{\frac{4}{3}}=1$.

From this equation it is clear that the $y-$ intercept is $\frac{4}{3}$.