Show that, given a ray AB, there is a coordinate system f on the line AB such that: ray AB = {P|f(P) >= 0}.

Here is what I have:

By definition ray AB is the union of the segment AB and the set of all points C such that A-B-C. Now, let L be a line and let P and Q be points on L. Let f be any coordinate system for L. Then let a=f(P) and for each point T of L, let g(t)=f(t)-a. Then this means that f is a coordinate system for L, and f(p)>=0. Therefore ray AB = {P|f(p)>=0}.

How is this? Is there any way that I can improve it?

Thanks for the help.