Proof of linear dependence of coplanar vectors

There is a theorem in my math book which proof I don't understand.

Theorem is: Vectors x,y,z are linear dependent if they are coplanar and two of them are collinear.

Proof:

1) Vectors x,y,z are in plane alpha.

2) Vectors x and y are collinear.

3) There is real number k != 0 such that y = kx

4) From 3) follows that y - kx + 0z = 0 which means that they are linear dependent.

I don't understand step 4). Where did come from 0z?

Can someone explain me step 4)?