The goal is to explain why two separate parallel lines determine a unique plane and how to derive the plane's equation using line equations.
Use the statement that a unique plane is determined by three non-collinear points to explain the outcome.
Choose two separate spots on one line and a third point on the other line. The three points that were picked are non-collinear.
A unique plane is determined by the three non-collinear points. The three points selected are noncollinear.
That's why the two distinct parallel lines determine a unique plane.