Consider the competing straights**:**

** r**: a_{1}x + b_{1}y + c_{1} = 0 **s**: a_{2}x + b_{2}y + c_{2} = 0,

They intersect at one point **Q**.

If **P**(x, y) is any point in any of the bisectors, PQ then **P** equidist of **r** and **s**:

Considering the positive sign, we get a bisector; considering the negative sign, we get the other one. Let's look at an example:

If **r**: 3x + 2y - 7 = 0 and **s**: 2x - 3y + 1 = 0, so your bisectors are: