Final answer:
To find the equation of the plane that contains the given line and is parallel to the plane, find a point on the given line and the normal vector of the parallel plane.
Step-by-step explanation:
To find the equation of the plane that contains the given line and is parallel to the plane, we need to find a point on the given line and the normal vector of the parallel plane.
The given line is x = 1, y = 2 - t, z = 4 - 3t. Taking t = 0, we get the point (1, 2, 4) on the line.
The normal vector of the plane 5x + 2y = 1 is (5, 2, 0).
So, the equation of the plane is 5(x - 1) + 2(y - 2) + 0(z - 4) = 0, which simplifies to 5x + 2y - 10 = 0.