Find intersection between 2 vectors

Hi guys…
Im sorry i have a bit of an embracing question… Is there a way for me just find the intersection of two straight line using Vector2f? I have two points a1, a2 in the scene graph, and another 2 point b1, b2. I would like to find an intersection of the two straight line a1-a2 and b1-b2. I would prefer not use ray casting…

something Mathamatical like
y = 3x-3 (a1-a2) and
y = 2.3x+4 (b1-b2)
3x-3 = 2.3x+4