There are many approaches to demonstrating this and also different ways in which poverty can affect a person's likelihood to committing criminal acts. Take society as a whole for example, the simple idea of a poorer or less fortunate person can often insight the idea of a criminal. If you think of an impoverished area and the people who live there, you may think of deviant individuals. This thought process itself plays a role in crime, take labelling theory, if you call a person X and you treat them like they are X, then they are going to act and become X because they are already being treated that way. So a person who lives in poverty who is treated as though they are a criminal, may as well act like a criminal because what do they have to lose?
Another thing could be location, those suffering through poverty are highly unlikely to be living in the most upstate parts of a city, they are more likely to live in crowded council areas that do not have much going on. This leads to people doing things such as graffitiing, drinking in public, criminal damage. Council estates are also great for drug dealers as poverty can cause people to want to disconnect from reality, drugs are great for doing that. There are also more people for them to target and sell too and a dealer is less likely to be seen as suspicious and thus reported in a rundown area than they are a nice rich area. All of this behaviour leads to gangs, gangs then lead to things such as knife crime.
Psychology can also play a role, again, a person more in poverty is going to have more untreated mental health issues, these can then lead to unlawful acts. Poverty is a huge issue when it comes down to crime, and it is for so many reasons. You can come at it from any angle and find a way that it links itself to crime in some aspect (prostitution, gambling, theft, car crimes etc)