posted by Henry .
determine the coordinates of two points on the plane with equation 5x + 4y - 3z = 6
let x=0, y=0, then z= -2 ---> (0,0,-2)
let x=1, y=0, then z = -1/3 -- (1,0,-1/3)
let two of the variables be anything you want, then solve for the third.
Just noticed that you had posted this before and Steve had answered you.
Please check your earlier posts before re-posting the same question again, to avoid unnecessary duplication of our efforts.