what was the importance of slim's relationship with the men?
Slim is the leader and he is said to move "with a majesty." The men come to Slim for advice. His words ring with authority, and they are obeyed.
"His authority was so great that his word was taken on any subject, be it politics or love."
George knows that because Slim is not a ranch hand like himself, this quiet man with "God-like eyes" has no pettiness about him. Unlike the other ranch workers, Slim does not need to vie for any position or compete for anything. When he first sees George and Lennie, Slim "look[s] kindly" at them. The tone of his voice is also friendly, "invit[ing] confidence without demanding it."
After Slim gives Lennie one of his pups that his dog has just whelped, George thanks him, telling Slim that Lennie will want to sleep with this puppy. Slim invites George's confidence as he continues to converse with him, seeming to take a personal interest in George. It benefits George to have someone with whom he can confide his feelings. They discuss Lennie and George's relationship with him. George speaks about their history, revealing to Slim what happened in Weed, the town they have just come from.
Later on, old Candy comes into the bunkhouse, followed by his old dog. When Carlson insists Candy let him put the old dog out of his misery, Candy sadly replies he has had the dog a long time and even herded sheep with him. He tells Carlson he cannot let his dog go. Carlson then offers to shoot it for Candy, and he tells the old swamper that Slim will let him have one of Lulu's pups. Candy refuses, and he looks to Slim for "a reversal." But Slim gives him none so Candy feels he must allow Carlson to take his old dog. The thoughtful Slim tells Carlson to take a shovel so that he will bury Candy's beloved pet.
Later, after Lennie inadvertently kills Curley's wife and George shoots Lennie, Slim seems to know the real reason George commits this act because of their first conversation. He understands George's rationale and grief. He consoles George by saying, "You hadda, George. I swear you hadda. Come on with me."