You are making it far too hard.
give an equation for the plane that is parallel to the plane 5x-4y+z=1 and that passes through the point (2,-1,-2).
i used the formula
f(a,b) + fx(a,b)(x-a) + fy(a,b)(y-b) + fz(a,b)(z-c)
(-5x+4y+1) + (-5)(x-2) + (4)(y+1) + (1)(z+2)
then plug in the points for the rest of the variables
-13 + (-5x+10) + (4y+4) + (z+2)
i'm pretty sure this is wrong and i'm not sure if i used the right formula for this. can anyone explain to me how to do this? is there a simpler way? thanks!