Final answer:
The linking verb in the sentence is 'became' and the verb is 'skates'.
Step-by-step explanation:
In the sentence "the new skates quickly became a popular item," the linking verb is became and the verb is skates.
Linking verbs are verbs that are completed by a subject complement, which describes or identifies the subject. In this sentence, "became" links the subject "skates" with the subject complement "a popular item."
Therefore, the correct answer is Linking: became, Verb: skates.