Learn Hardcore Japanese: sensei ha isogasii desu.

は is the topic‐marking particle. It tells you that 先生 (the teacher) is what the sentence is about. The rest of the sentence gives information or makes a statement about that topic.

What role does です play at the end of the sentence?

です is the polite copula, roughly equivalent to “is” in English. It makes the statement polite and completes the sentence. Without it (in casual speech), the sentence would sound more informal.

What kind of word is 忙しい, and why does it come before です?

忙しい is an い-adjective. In Japanese, い-adjectives can directly modify nouns (e.g. 忙しい先生 “busy teacher”) or serve as predicates when they’re followed by です, turning them into polite statements.

Why isn’t there a subject like “he” or “she” in this sentence?

Japanese often omits pronouns when the context is clear. Here, by marking 先生 with は, you already know who you’re talking about, so there’s no need to say “he” or “she.”

Can you drop 先生は and just say 忙しいです?

Yes. If the topic has been established in conversation, you can omit 先生は and simply say 忙しいです, meaning “(He/She/They are) busy.” The listener infers who you mean.

How do you change this sentence into the past tense or turn it into a question?

– Past tense: Replace the adjective ending い with かった and add です → 先生は忙しかったです。
– Question: Add the question particle か at the end → 先生は忙しいですか？

How would you say this casually among friends?

In casual speech you can drop です:
– 先生は忙しい。 (“The teacher is busy.”)
Or even shorten further if context is clear:
– 先生、忙しい？ (“Teacher, busy?”)