2020-II-26

Ans: D
The slope of $L$

$\begin{array}{cl}=& {\displaystyle \frac{-k}{4}}\end{array}$

The slope of the straight line $6x-9y+4=0$

$\begin{array}{cl}=& {\displaystyle \frac{6}{9}}\\ =& {\displaystyle \frac{2}{3}}\end{array}$

Since $L$ is perpendicular to the straight line $6x–9y+4=0$, then we have

$\begin{array}{rcl}{\displaystyle \frac{-k}{4}}\times {\displaystyle \frac{2}{3}}& =& -1\\ k& =& 6\end{array}$

Therefore, the equation of $L$ is $6x+4y-12=0$.

Hence, the $y$-intercept of $L$

$\begin{array}{cl}=& {\displaystyle \frac{12}{4}}\\ =& 3\end{array}$