Angle Between Two Straight Lines

Let L1 and L2 be the two intersecting lines and assume that P be the point of intersection of the two straight lines which makes angle θ1 and θ2 with the positive direction of x-axis.

L1: y = m1x + c1

L2: y = m2x + c2

m1 = tan θ1

m2 = tan θ2

Let θ be the angle between the two straight lines.

θ1 = θ + θ2

θ = θ1 − θ2

tan θ = tan (θ1 − θ2)

Parallel Lines

If the two straight lines are parallel, then their slopes are equal.

m1 = m2

If the straight lines are parallel, then the coefficients of x and y are proportional in their equations. In particular, the equations of two parallel straight lines differ only by the constant term.

Perpendicular Lines

If the two straight lines are perpendicular then the product of their slopes is −1.

1 + m1m2 = 0

m1m2 = −1

The equation of the straight line perpendicular to the straight line ax + by + c = 0 is of the form bx − ay + k = 0 for some k.