Hi! It depends on the what you are trying to say, in day to day life I would often use both expressions. Although I would make a slight revision, and change both to: 1. People on a low income 2. People with a low income It just slightly more natural to me! :)

Hello! Prepositions and grammar can be confusing at times 🙈 it happens to the best of us. I would say “People on low incomes” is the correct way. I would use “with” if you were saying “ people with lower incomes are less likely to have access to internet” just an example. Message me if you need more help.

You may have identified a British English versus US English divergence. As such you, you can be happy to hear that you can get away with saying either (and both): Consider them as interchangeable. Your homework is to remember (reading through the comments) which one is preferred by British English native speakers. Yes, that's right!!!! You listed it as number 1 for a very good reason.

Is that an elementary one that you've got for us?

Hello. Your questions are far from elementary, we are glad to help. It's more natural to say, "People with low income." Regards