Denise slipped on the ice patch behind her garage is this sentence transitive or intransitive

The correct answer is intransitive.

A verb can be either transitive or intransitive, depending on whether it needs a direct object or not. The verb to slip in the sentence above doesn't need an object (you won't ask - Denise slipped what?), which means that it is an intransitive verb.

A transitive verb is, for example, to write. - I am writing a book.