How to make smooth line movement?

Hello!
I've been searching it everywhere, but couldn't find anything in the net. I want to make smooth line movement. I've tried to create motion, but line just moves, and I want it to move smoothly according to the path. What I want to achieve can be seen here:
http://www.noartistname.com/demo/
But that's what I did so far - made movement out of several broken lines - how can I make more smooth movement?
Thanks,
Aleks.

the easiest for non-coders is to tween a mask of the full line. you can also use the flash drawing methods but that takes some coding. see:
www.kglad.com , click snippets, function graphs.

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