Trying to figure out which is the correct answer because I am finding two different one. -4x+8z=16 is the equation of the plane. The question I am trying to figure out is what is the point of intercept with the y-axis? Any help would be appreciated!
Are you trying to answer this using Wolfram Alpha or Mathematica? If yes, what have you tried? If not, this is not a forum for homework or general math questions, only for the use of Wolfram software systems. In any case, your equation just defines a line, not a plane as you wrote it.
y can be anything, so I think this defines a plane.
The y-axis intercept is where x=0 and z=0,
-4*0 + 8*0 = 16
0=16
Simple.
Perhaps extra dimensions would help. Maybe a job for string theory?