The question is really asking for a plane parallel to the plane:
which passes through the point (0,1,1).
To get the equation of a plane, you want a vector normal to the plane, and a point on the plane. We already have a point on the plane (0,1,1).
To get the normal vector of the plane, look at the coefficients of the x, y, and z, in the equation. Your normal vector is <1,1,1>
(If your plane were 2x+3y+4z=5, the normal vector would be <2,3,4> )
The equation of the plane, then, is:
The outer multipliers are the normal vector, the subtracted pieces are the point. The right side is always 0.
This simplifies to: