I was solving a problem. In

Question

It r have been given that two lines are perpendicular to each other
The equation of one line
2x-3y+4=0

Now i have to find the equation of another line

We can find it by finding the slope of the abovementioned line( the other line)

But we are prohibited to do so
I have to find the equation of other line

So
Equation of line perpendicular to
ax+by+c=0
Is
bx-ay+c=0
Now I am confused whether we have to take the negative sign which is in front of b (is -3 here) in perpendicular form
And what Is the equation

Answer 1

ax+by+c=0 ----> bx-ay+c=0

What that says is :
interchange the coefficients of the x and y terms
then change the sign of the y term to its opposite.
Remember, it is considered to be "good form" to have the x term at the front as a positive term.

e.g.

5x + 7y + 9 = 0 , a perpendicular line would be
7x - 5y + C = 0

yours:
2x-3y + 4 = 0 ----> 3x + 2y + 4 = 0

I kept the constant at 4, it could have been anything.
The constant could be anything else and the new line would still be perpendicular, since the constant has no effect on the slope of a line.

Answer 2

Ahh interchange of coefficients of x and y and sign change of y

Now I get it