# Choose the correct answer from the given four options. A line passes through (2, 2) and is perpendicular to the line $3x + y=3$. Its y - intercept is

$\begin {array} {1 1} (A)\;\large\frac{1}{3} & \quad (B)\;\large\frac{2}{3} \\ (C)\;1 & \quad (D)\;\large\frac{4}{3} \end {array}$

Toolbox:
• Slope of a line which is perpendicular to a line having slope 'm' is $- \large\frac{1}{m}$.
• Equation of a line having slope $m$ and passing through $(x_1, y_1)$ is $(y-y_1)=m(x-x_1)$
Step 1 :
Equation of the given line is $- \large\frac{3}{1}$$= -3 Hence slope of the line which is perpendicular to the above line is \large\frac{1}{3} It is given that the line passes through the point (2,2) Hence equation of the required line is (y-2)=\large\frac{1}{3}$$(x-2)$
$\Rightarrow 3y-6=x-2$
(i.e) $3y=x+4$