Is it illegal to use a trademarked slogan if there is no profit involved The specific law would be very appreciated?

Using a trademarked slogan without permission can still lead to legal issues, even if there is no profit involved. Under the Lanham Act (15 U.S.C. § 1051 et seq.), trademark infringement can occur if the use creates a likelihood of confusion among consumers regarding the source of goods or services. Non-commercial use may have some defenses, such as fair use or parody, but this can be context-dependent and may still lead to legal challenges. It is advisable to seek legal counsel if you're considering using a trademarked slogan.