I have a web cam at home and wanted to know if it was possible to broadcast live from my camera straight to my website.

Of course, we are all clairvouyant, mind reading geniuses, and we know what your webcam is, what software came with it, what connection you have to the internet and what and where your website is!

or to put it another way;
A little more information would be useful

I think help can be given without all the details.

It's a funny thing, that this is the same problem that I encountered just yesterday. Found one on sf.net.

DCAM, opensource: http://sourceforge.net/projects/dcamserver
Here is a list of "live streaming" software (beware, adult ads)

This will get you started

maedi