A linking verb connects the subject of a sentence to a predicate noun or predicate adjective.
* Predicate noun: A noun that renames or identifies the subject. Example: "The cat is a fluffy persian." ("Persian" is the predicate noun, renaming "cat")
* Predicate adjective: An adjective that describes the subject. Example: "The cat is fluffy." ("Fluffy" is the predicate adjective, describing "cat")
Therefore, a sentence containing a linking verb will always have a predicate noun or predicate adjective.