Q118 / 180 · KCET 2015 · Mathematics

A line passes through \( (2,2) \) and is perpendicular in the line \( 3 x+y=3 \) its \( y \)-intercepts is

  • A
    \( \frac{1}{3} \)
  • B
    \( \frac{2}{3} \)
  • Correct answer
    C
    \( \frac{4}{3} \)
  • D
    \( 11 \)

Solution

Given line, $3 x+y=3$ $\Rightarrow y=-3 x+3$ So, slope of this line is $m_{1}=-3$ Then, slope of line perpendicular to this line is $m_{2}=\frac{1}{3}$ General equation line passing through point $\left(x_{1}, y_{1}\right)$ is $\left(y-y_{1}\right)=m\left(x-x_{1}\right)$ Here $m=\frac{1}{3}$ and $\left(x_{1}, y_{1}\right)=(2,2)$. So, $y-2=\frac{1}{3}(x-2)$ $\Rightarrow y-2=\frac{x}{3}-\frac{2}{3}$ $\Rightarrow y=\frac{x}{3}+2-\frac{2}{3}$ $\Rightarrow y=\frac{x}{3}+\frac{4}{3}$ So, $y$-axis intercept is, $\frac{4}{3}$

Hence, the correct answer is option: 'C'.

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