I would like to see a picture of the piping to the "left" of the disposer, because I am not sure what that "Y" is doing, or why the sink vent turns sideways in that direction. Whoever did the plumbing did not do you any favors because there should have been a cleanout in the line between the tee and they Y. OWNING a $200.00 snake machine, and KNOWING how and where to use it are often two distinctly different animals. The only $200.00 snake I own is a hand held battery operated one for small lines. For a line like yours, I use my $2,000.00 machine.