Question

The image of the point (1,3,4) in the plane 2x-y+z+3 is what?

Answer 1

use a graphing calculator

Answer 2

First, that's not a plane. If you had written "=0", I would feel better about it.

Have you considered tracing the Normal Vector from the point until you find the plane?

x = 1 + 2t
y = 2 - t
z = 4 + t

See if you can find t = -7/6. Then what?