How to verify a plane is parallel to a line?

Question

Plane equation is: $$7x-5y+2z-9=0$$

Line parametric form: $x=t, y=-4+3t, z=9-4t$

Answer 1

1. Construct the surface normal of the plane, $\hat{n}$
2. Find the vector direction of the line, $\vec{v}$
3. If $\hat{n} \cdot \vec{v} = 0 $, then the surface normal is perpendicular to the line, so the line is parallel to the plane

Answer 2

You could just substitute for $x$, $y$ and $z$, and see if there's any solutions.