Question

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

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

Answer 1

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

Equation of the line in slope-intercept form is $y=mx+c$
The line passes through $(2,2).$
$\Rightarrow 2=2m+c$
$\Rightarrow m=\frac{2-c}{2}$
The line is perpendicular to $3x+y=3\text{i.e.,}y=-3x+3$
Slope of $y=-3x+3$ is $-3$.
$\therefore -3\times \left(\frac{2-c}{2}\right)=-1$
$\Rightarrow c=\frac{4}{3}$
Thus, the y-intercept of the line is $\frac{4}{3}.$