Question

How do you write an equation for a a line perpendicular to a line with only having the equation and not graphing?

Answer 1

Perpendicular lines gradients times to get -1 so you just use a line with any y intercept but the gradient must times with the gradient you already have to get minus one.

Answer 2

Put each formula in y=mx+b form, then find the inverse of m.  
Ex: 
1. x+y=2
y=x-2
the inverse of 1 is -1 so the perpendicular line would be y=-x-2