Find parametric equations of the plane $3x+4y-2z=4$?

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I have no idea what initial point to use for planes since I'm not familiar with plotting graphs of $(x,y,z)$.

My points are

  • $P_1 = (0,1,0)$
  • $P_2 = (4/3, 0, 0)$
  • $P_3 = (0, 0, -2)$

I calculated the positions vector which I got

  • $P_1P_2 = (\frac43, -1, 0)$
  • $P_1P_3 = (0, -1, -2)$

My vector equation then was $[x,y,z] = [0, 1, 0] + [4/3, -1, 0]s + [0, -1, -2]r$
and then I just read off this to get the parametric equations

$$x = 4s/3,y = 1-s-r,z = -2\cdot r$$

How can I determine the initial point for planes?