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) 2/3
(c) 1
(d) 4/3

Answer 1

(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 $\frac{4}{3}$.