Complete the sentence with the appropriate form of the given verb:
They've invited me to their house. They ___________ (be) offended if I don't go.

The sentence "They've invited me to their house. They will be offended if I don't go." uses the future tense. The future tense is formed using the auxiliary verb "will" followed by the base form of the main verb (be). It is used to talk about actions that will happen in the future.

In this sentence, "will be" indicates that the feeling of being offended will occur in the future if the speaker doesn't go to their house, as implied by the context of the sentence.

In the other options:
Option A: are being (present continuous) is not suitable for indicating a future consequence of not going to their house.
Option C: are (simple present) is not suitable for indicating a future consequence of not going to their house.
Option D: have been (present perfect) is not suitable for indicating a future consequence of not going to their house.

The correct answer is Option B: will be, which accurately conveys the future consequence of the potential offense if the speaker doesn't go to their house.