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The particle 가 marks 회의 as the grammatical subject—the thing that “is being held.” If you used 은/는 (as in 회의는 온라인으로 진행돼요), you’d shift the nuance from simply stating a fact to “As for the meeting, it’s held online,” putting emphasis or contrast on 회의.

What role does 온라인으로 play, and why do we use 으로 instead of 에 or 에서?

으로 here indicates the means or method: “by/through online.”

에 would mark a static location (“at”), but 온라인 isn’t treated as a physical place.
에서 also marks location of an action, but when you want to say “via/through the internet,” you use 온라인으로.

What does the verb 진행되다 mean, and why is it used here instead of 진행하다?

진행되다 is the passive/intransitive form of 진행하다 (“to carry out, to conduct”).

진행하다 (active): “Someone conducts the meeting.”
진행되다 (passive/intransitive): “The meeting is conducted.”
Since the focus is on the meeting itself (it’s being held), we use 진행되다.

Why is it 진행돼요 instead of 진행되어요?

진행되어요 contracts in spoken and polite written Korean to 진행돼요.

Full form: 되 + 어요 → 되어요
Contracted: 되어요 → 돼요
This contraction is standard in everyday polite speech.

Could I say 회의가 온라인으로 진행해요 instead?

진행해요 is the active form of 진행하다 and would imply “(we) conduct the meeting online,” focusing on the agent doing the action.

회의가 온라인으로 진행돼요: “The meeting is held online.” (intransitive/passive)
회의를 온라인으로 진행해요: “(We) hold the meeting online.” (transitive/active; note the object particle 를)

Does 진행돼요 express an ongoing action like “is happening right now”?

Not necessarily. It’s the simple present (polite), so it can mean “takes place/gets held” generally or on a schedule.
To emphasize “right now, in progress,” you’d say:
회의가 지금 온라인으로 진행되고 있어요.

Can I rearrange the word order, for example, 온라인으로 회의가 진행돼요?

Yes. Korean is relatively flexible:

회의가 온라인으로 진행돼요. (neutral statement)
온라인으로 회의가 진행돼요. (puts more emphasis on the method 온라인으로)
Both are grammatically correct; the fronted element receives greater focus.

What level of politeness does the ending -요 convey, and how would it change in other styles?

The -요 ending is polite informal (commonly used in everyday speech with strangers or colleagues).

More formal: 회의가 온라인으로 진행됩니다.
Casual (among close friends/family): 회의가 온라인으로 진행돼.

Could you drop the particle 가 and just say 회의 온라인으로 진행돼요?

In very casual speech or notes, Koreans sometimes omit particles, but in standard sentences you need 가 to mark the subject clearly. Omitting it can sound clipped or ambiguous, so it’s best to keep 회의가 온라인으로 진행돼요.