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. $1$
• D. $\frac{4}{3}$

Answer 1

The correct option is D

$\frac{4}{3}$

The explanation for the correct option:

Find the $y$ - intercept of the line:

Slope of line $3x+y=3$ is $m_1=-3$

Slope of perpendicular line, $m_2=\frac{1}{3}$ $\left[\mathbf{\because }{\mathit{m}}_{\mathbf{1}}{\mathit{m}}_{\mathbf{2}}\mathbf{=}\mathbf{-}\mathbf{1}\right]$

$\therefore$Equation of line passing through $(2,2)$ with slope $\frac{1}{3}$ is

$\begin{array}{rcl}(y–y_1)& =& m(x–x_1)\end{array}$

$\Rightarrow$$\begin{array}{rcl}(y–2)& =& (⅓)(x–2)\end{array}$

$\Rightarrow$ $\begin{array}{rcl}y& =& (⅓)(x–2)+2\end{array}$

$\Rightarrow$ $\begin{array}{rcl}y& =& (⅓)x+4/3\end{array}$

$\therefore$$\mathit{y}$ intercept, $\mathit{c}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{4}}{\mathbf{3}}$

Hence option D is the answer.