Question

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

Answer 1

Question :-

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

Answer :-

$\to \boxed{ \sf \: p = \frac{2}{3} } \:$

To Find :-

→ Value of "p" .

Explanation :-

If we have two lines are both are perpendicular to each other then product of their slope is -1

Solution :-

We have ,

→ y = 3x + 7

compare to y = mx + c

→ m = 3 ,

slope of line 1 is m = 3

now ,let "n" be the slope of another line,

$\to \sf \: 2y + px = 3 \\ \\ \to \sf 2y = - px + 3 \\ \\ \to \sf y = \frac{ - p}{2} x + 3 \\ \\ \sf compare \: with \: y \: = nx \: + c \\ \\ \to \sf \: n = \frac{ - p}{2}$

° • ° Both lines are perpendicular to each other , hence,

$\to \sf \: m \: n \: = - 1 \\ \: \\ \to \sf - 3 \times \frac{p}{2} = - 1 \: \\ \: \\ \to \sf 3p = 2 \\ \\ \to \boxed{\sf p = \frac{2}{3} }$