Perpendicular equations?

Question

Please explain to me how to find a perpendicular equation (if there is such thing), for an example equation, like 2x+5x=10.

Thanks.

Answer 1

let us consider a more general eq.
Ax+By=C
the slope of this eq is -A/B(=m,say)
Now for 2 perpendicular lines (eqns), m.n=-1 where m and n are their respective slopes.
So the slope of an eq. perp. to the one given is n=-1/m=B/A in this case.
so the perp eqn is
Bx-Ay=D where D is a real

Answer 2

7x = 10
x = 10 / 7
This is a vertical line that passes thro`(10/7,0)
Lines perpendicular to this line will have gradient = 0.
These are horizontal lines and example equations are:-
y = 1
y = 4
y = - 5
etc