Suppose we have a Line:

P = P1 + tL

and a plane:

N • (P - P2) = 0

We can substitute P into the plane equation:

N • (P1 + tL - P2) = 0

Solve for t:

t = (N • (P2 - P1)) / (N • L)

The point of intersection is:

P = P1 + ((N • (P2 - P1)) / (N • L)) L