Question

If the lines $2x-by+5=0$ and $ax+3y=2$ are parallel, find the relation connecting $a$ and $b$.

Answer 1

We have

$2x-by+5=0$

and, $ax+3y=2$

Now,

$2x-by+5=0$

or, $by=2x+5$

or $y=\frac{2x}{b}+\frac{5}{b}$

Slope of this line $=\frac{2}{b}$

Again

$ax+3y=2$

$3y=-ax+2$

$y=\frac{-ax}{3}+\frac{2}{3}$

Slope of this line $=\frac{-a}{3}$

$\because$ The lines are parallel, both slopes of the two lines are equals.

$\therefore \frac{2}{b}=\frac{-a}{3}orab=-6$

Hence, which is the required answer.