Final answer:
Jackie is using the foot-in-the-door technique of persuasion by first asking for a new iPhone (knowing it will be denied) and then asking for a new phone case.
Step-by-step explanation:
The persuasion technique being used by Jackie is the foot-in-the-door technique. In this technique, the persuader first makes a small request that they know will be accepted, and then follows it up with a larger request. By asking for a new iPhone first, Jackie knew her mom would deny the request.
However, she then asked for a new phone case, which her mom agreed to. The phone case was actually what Jackie wanted all along. By first making a request that she knew would be denied, Jackie increased the likelihood of her mom agreeing to the smaller request for the phone case.