This sentence appears not to be complete. First, it has no subject, but it does have a verb. The incomplete sentence would look like this" __________ heated by solar energy have special collectors on the roofs to trap sunlight." A plural subject is the only thing that is missing in the sentence.
"Home is" wrong because it is a singular subject, while a plural subject is what is required. "Homes are" though it has a plural subject; it is wrong because it has a verb. "A home" is also wrong because it is a singular subject, and what the sentence requires is a plural subject.
"Homes” is the only correct option. The sentence will be logical and make a complete sense if it is placed in the sentence. "HOMES heated by solar energy have special collectors on the roofs to trap sunlight."
The sentence is incomplete, it does not have a subject but has a verb. The incomplete sentence is " __________ heated by solar energy have special collectors on the roofs to trap sunlight". The only thing missing is the 'Plural subject'
"A home is"is wrong because it is a singular subject and it has a verb.
"Homes are" is wrong because it has a verb, the sentence already has a verb.
"A home" is wrong because it is a singular subject and the sentence needs a plural subject.
"Home" is the only one with a plural subject without a verb. If it is placed in the sentence. The sentence is complete.
"HOMES heated by solar energy have special collectors on the roofs to trap sunlight".