1. Brian walked (slowly) home, as the day was so warm and pleasant.
Slowly is an adverb, because walked is the verb in the sentence and slowly is describing how Brian walked.
Adverbs describe verbs so this is why slowly is an adverb. The correct answer is C. Adverb.
2. I would rather be (sleeping)!
First off, you can cross out the last two options because sleeping is definitely not an infinitive.
Infinitives always have the word "to" and then a verb, such as "to sleep" or "to run". So sleeping must be a gerund (noun).
Gerunds usually function as nouns, therefore your answer is A. It is a gerund functioning as a noun.
