Say you have 2 lines in the plane. You are given their slopes.

The angle between 2 lines in the 2D cartesian plane is given by:

tan( a ) = | (m₂ – m₁) / (1 + m₁m₂) |

If the lines are perpendicular, then

m₁m₂ = -1

and so

(1 + m₁m₂) = 0

then a = 90 degrees and the lines are perpendicular.