Question

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

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

Answer 1

Answer: (B)

$4/3$

The slope of the line $3x+y=3$ is $-3$

Then, slope of the line perpendicular to this line must be $\frac{1}{3}$

The equation of the line passing through $(2,2)$ and having aslope of $\frac{1}{3}$ is

$(y-2)=\frac{1}{3}(x-2)$

$⟹3y-6=x-2$

$⟹x-3y+4=0$

$⟹y=\frac{x}{3}+\frac{4}{3}$

Then, $y$-intercept of this line is $\frac{4}{3}$