Я быстро иду к выходу.

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Breakdown of Я быстро иду к выходу.

• быстро: quickly
• идти: to walk
• выход: the exit

Questions & Answers about Я быстро иду к выходу.

Why is it иду and not хожу?

Because идти / иду is the verb used for going in one direction right now.

• Я иду к выходу = I am going toward the exit now.
• Я хожу к выходу would not fit this situation well, because ходить usually means:
  • going habitually
  • going back and forth / around
  • going in no single clear direction

This is one of the most important Russian verb pairs:

• идти = to go on foot, one-way, at this moment
• ходить = to go on foot regularly, repeatedly, or in various directions

So in this sentence, иду is the natural choice.

Why is выходу used instead of выход?

Because the preposition к requires the dative case.

The dictionary form is:

• выход = exit

After к, it changes:

• к выходу = toward the exit / to the exit

So:

• к
  • dative

This is a very common pattern:

• к дому = toward the house
• к двери = toward the door
• к другу = to a friend

That is why выход becomes выходу.