Proof for: if x<y and z>0, then xz<yz

[tmmclaug]

I need to figure out a proof for it x<y and z>0, then xz<yz. However, the proof has to use the properties of an ordered field. Any help would be greatly appreciated.

 

[daon]

If x<y then (y-x)>0. Assuming z>0, what do you know about the product z(y-x)?