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. $\frac{1}{2}$

Answer 1

The correct option is D

$\frac{1}{2}$

Explanation for the correct option:

Step 1: Finding the slope:

The equation of straight line is

$$\begin{gathered} 2x+y=3 \\ y=-2x+3...\left(1\right) \end{gathered}$$

On comparing equation $1$ with the general form of equation $y=mx+c$, we get

The slope, $m=-2$

For the perpendicular lines, the slope, $m{m}_1=-1$

$$\begin{gathered} \Rightarrow -2m_1=-1 \\ {m}_1=\frac{1}{2} \end{gathered}$$

Step 2: Finding the y-intercept.

The equation of line passes through the point is $(y-y_1)=m_1(x-x_1)$

The perpendicular line passes through the point $(1,1)$ and slope $m_1=\frac{1}{2}$ is

$$\begin{gathered} \Rightarrow (y-1)=\frac{1}{2}(x-1) \\ \Rightarrow y=\frac{1}{2}x-\frac{1}{2}+1 \\ \Rightarrow y=\frac{1}{2}x+\frac{1}{2} \end{gathered}$$

On comparing this with the general form $y=mx+c$, we get,

The y-intercept as $c=\frac{1}{2}$.

Hence, option (D) $\frac{\mathbf{1}}{\mathbf{2}}$ is the correct answer.