Brief recap (so the decision makes sense): In Chapter 6, after Lennie accidentally kills Curley's wife, he goes to the riverbank — the place George told him to go if he got into trouble. George finds Lennie there and, to spare him from a worse fate at the hands of Curley and the other men, George shoots Lennie himself. This is George's painful, deliberate act of mercy.
What do Slim and George decide to do?
George makes the decision to shoot Lennie alone — Slim does not make that choice for him. George carries out the act to prevent a brutal lynching and to give Lennie a peaceful, quick death.
Afterward, Slim immediately understands why George did it. He does not accuse or shame George; instead he comforts him. The closing scene shows Slim putting his arm around George and saying, "You hadda, George. I swear you hadda." They then leave the ranch together — Slim supports George and helps him through the immediate aftermath (Slim leads him away to get something to drink and offers quiet companionship).
What bond do they have?
Respect and understanding: Slim is the most respected worker on the ranch and the one who truly understands the moral difficulty of George's choice. He recognizes that George acted out of compassion, not malice.
Compassion and emotional support: Slim offers George comfort rather than judgment. His sympathy gives George the only human consolation available in that moment.
A quiet, brotherly connection: Their bond isn't described as an old friendship, but as a human tie based on mutual respect, shared values, and the ability to understand painful responsibility. Slim becomes the person who shares George's burden in the final scene.
In short: George decides (and acts) to kill Lennie as a mercy; Slim doesn't decide that action but recognizes its necessity, comforts George, and walks away with him. Their bond is one of deep empathy, respect, and supportive companionship in a moment of harsh moral choice.