Another Summoner Ranting About Salty People.

Okay, I know the ability to mute people is probably the best thing Riot has ever done in this game, but I want to help my teammates out the same way. I've seen way to many people who are worth muting and makes our teammates go on tilt, despite they're doing fine, how do I keep them happy? On a related note, how do I keep the person who's flaming them happy? I don't know the amount of ranked games I've lost about this but I know I want to change it, any tips? x.x