If you want to write an expository paragraph about how Roger is poor, you need to look for textual evidence that makes you think he's poor. As you read the story, you ran across clues that gave you that impression. It's a good idea to underline (or make notes of) parts of any story or poem that help you answer questions like this, even if you have to read the story twice.
In this case, you might have noticed that she asked him if there was anyone at home to tell him to wash his face, and he said, "No'm." His dialect could be linked to his being poor--more likely, uneducated--but having no one at home is not a characteristic of well-to-do children. It is most often part of the lives of poor children. They may have only one parent who works all the time, or who neglects them willfully.
The narrator describes him as "willow-wild," also suggesting that he has no one to teach him how to behave. The fact that he's out alone at 11pm alone (snatching purses) suggests a young man from a poorer family. Moreover, he is trying to get the money to buy blue suede shoes. He isn't necessarily going hungry--he wants something that makes him look less poor. This fits in with the fact that being poor is its own stigma, and the poor often do what they can to appear like they aren't poor.