Question

A straight line perpendicular to the line $2x+y=3$ is passing through $(1,1)$. Its $y$-intercept is

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

Answer 1

Answer: (D)

$\frac{1}{2}$

Given equation of line is $2x+y=3$

$m=-\frac{2}{1}=2$

Let slope of line passing through $(1,1)$ be $m^{\prime }$

$m{m}^{\prime }=-1\Rightarrow -2m^{\prime }=-1\Rightarrow m^{\prime }=\frac{1}{2}$

So, the equation of line is

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

For $y$ intercept $x=0$

$\Rightarrow 2y-0=1\Rightarrow y=\frac{1}{2}$

So, option D is correct.