Is this an example of age discrimination against this elderly person?She is 69 years old woman and lived alone. So she has to buy food for herself....

There is no definitive proof of age discrimination just
given the facts as you state them.  It might be happening, but it is not necessarily
going on.

The only place where discrimination may be taking
place is in the actions of the cashier.  When the cashier makes the old lady go to the
back of the line, she may be discriminating on the basis of age.  However, in order for
this to be age discrimination, you would need to see how the cashier treats people who
are not old but who pay slowly.

It would not be
unreasonable for a cashier to be unhappy with a slow customer.  Such a customer makes
everyone else in the line unhappy because they have to wait long periods of time.  This
would hurt the store's business.

So -- if the cashier makes
people wait when they are slow, that's fine.  But the cashier must make anyone wait --
an old person, a person with a baby who can't pay quickly because of having to hold the
baby -- anyone who's slow -- not just an old person.