Parallel plane containing a line

[TG3]

Homework Statement
Find the plane that contains the line x=3+2T, Y=t, Z=8-t and is parallel to the plane 2x + 4y +8z =17.

The attempt at a solution

It seemed to me that since the plane is parallel to the plane 2x+4y+8z=17, it must be of the form 2x+4y+8z+D=0 so that it would be parallel.
(Is that true?)

Anyways, I then converted the equation of the line out of parametric into (x-3)/2 = Y = -(Z-8).
(I know that part's right.)

But now I'm not sure what to do. Ideas?

 

[Dick]

Yes, your parallel plane equation is correct. Now just substitute x, y and z from the line equation into the plane equation and figure out what D must be.

 

[HallsofIvy]

It is, in fact, sufficient to use a single point on the line. Do you see why? For example, it should be easy to find D such that (3, 0, 8) (taking T= 0 in the equations of the line) is on the plane.