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. She always bought food in a small supermarket which is close her house. But she did not go to this Supermarket every week, she bought her food twice a month and she bought her food at early morning. The reason why she has to do this way is because she had bad experiences with cashier who works in this supermarket. The cashier complained she paid too slowly and delay her time to charge for another people. The cashier let she wait in line at last one when every time she want to pay her food. In fact, she tried to get her money and paid faster as she can. Anyway, she do not want to wait more than half hour that just for paying food based she wait in line. So, she bought her food twice a month and bought her food on the early morning that cashier do not have any reason to complain and pay on time.
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.