Question

Find the value of $k$ so that the line $2x+ky-9=0$ may be perpendicular to $2x+3y-1=0$.

Answer 1

Given:$2x+ky-9=0$ .......$\left(1\right)$

Slope of line $\left(1\right)=-\frac{coefficientofx}{coefficientofy}=-\frac{2}{k}$

Given:$2x+3y-1=0$ .......$\left(2\right)$

Slope of line $\left(2\right)=-\frac{coefficientofx}{coefficientofy}=-\frac{2}{3}$

As the lines $\left(1\right)$ and $\left(2\right)$ are perpendicular, the product of their slopes$=-1$

$\Rightarrow \frac{-2}{k}\times \frac{-2}{3}=-1$

$\Rightarrow \frac{4}{3k}=-1$

$\Rightarrow 4=-3k$

$\Rightarrow k=\frac{-4}{3}$