How we cite our quotes: (Act.Line)
Quote #4
YELENA ANDREYEVNA: So you've been drinking again today? Why?
VOYNITSKY: At least it offers one something like life… Don't stop me, Hélène!
YELENA ANDREYEVNA: You never used to drink, and you never used to talk so much… Go to bed! I'm bored with you. (2.171-76)
Through this exchange, we can see that the relationship between Yelena and Vanya used to be good. She says "you never used to…" as though he really used to be a different person. And now he is someone who needs to drink because he feels as though he doesn't have a life. That means a pretty big change has occurred.
Quote #5
ASTROV: [....] [Inspects the bottles on the table.] Medicines. What a lot of prescriptions! From Kharkov and Moscow and Tula… He's plagued every city with his gout. Is he mill or malingering? (2.219-22)
Kharkov, Moscow, and Tula were all important cities in Russian territory (Kharkov is in Ukraine). Serebryakov is getting his medicine from all the regional capitals, which could mean that his sickness is hard to cure and he's had to go to lots of doctors, or that he likes his drugs and spreads out of his doctor visits to get more prescriptions.
Quote #6
ASTROV: [...] You see, I'm drunk too. I usually get this drunk once a month. When I'm in this condition, I become extremely aggressive and ambitious. I can do anything then! I take on the most difficult operations and do them perfectly; I draw up the grandest plans for the future; I don't then think myself an eccentric, and I can believe I am bringing colossal benefits to mankind—colossal! (2.235-41)
He's the King of the World. Astrov feels like he can do anything when he drinks vodka till he's drunk, which he does about once a month. We can extrapolate that the rest of the time he must not feel that way, otherwise he wouldn't get drunk. So we can further conclude that Astrov feels powerless, and that's why he drinks.