Problem
Liz Lemon worked as a television news anchor for Channel 31. She and her boyfriend had been dating for four years. They both made plans to spend two weeks in Florida, which happened to be around the same time that most schools were on spring break. While on vacation with her boyfriend in Florida, Liz participated in a "wet t-shirt" contest that was videotaped without her consent by Dream Girls, Inc. and was licensed to Fun & Sun, Corp., which runs a Web site for adult entertainment through a subscription service on the Internet. Fun & Sun used depictions of Liz in its advertisements to promote the materials and services it markets. Web site searches related to Liz were the most popular search on the World Wide Web in 2017. She resigned from her position with Channel 31 because of the publicity and sought an injunction against defendants Dream Girls and Fun & Sun from using her image in any manner that promotes the sale of their goods or services. Defendants contend that the injunction would violate their First Amendment rights. What legal theory would Liz rely on to seek the injunction and would the injunction violate defendants' First Amendment rights?