Question

If the lines $y=3x+7$ and $2y+px=3$ are perpendicular to each other, find the value of $p.$

Answer 1

Given line equations,

$y=3x+7$

Slope of this line $=3$

And,

$2y+px=3$

$2y=-px+3$

$y=(-p/2)+3$

So, the slope of this line $=-p/2$

For these two lines to be perpendicular to each other, the product of their slopes must be $-1.$

$\left(3\right)\times (-p/2)=-1$

$3p/2=1$

$p=2/3$