"You are my boy."
"Vous" is formal, but also rarely used with children. A parent addressing his/her child would NEVER use "vous".
In that case, the king and queen would be saying it, and because they are higher in rank, they'd still use 'tu es'.
What if this is not a child? Could an adult say this to a grown man? I say this to my male friends all the time in English when they do something agreeable. I need something they produce it I will tell them "YOU are my boy!" give them a high five or something....maybe? Or maybe my favorite waiter?
I think Duo is more concerned with sentences being technically correct than socially plausible. "Vous êtes mon garçon" is technically correct, even if it's a weird thing to say.
Why is "Vous etres mon garcon" correct? Why not: "Vous etres mes garconS?"
adjectives agree with the noun they modify: "my" is modifying "boy". Since "boy" is singular, you must use "garcon", and since "garcon" is singular, you must use "mon".
My question is exactly, why is the word "garcon" is in singular after "vous". "Vous etres" implies, that there is not only one boy, but more, doesn't it? (but Duo said, it is also a correct solution to say: Vous etres mon garcon). Thanks!
'Vous' forms can be plural or they can be polite-singular. Since the example says 'my boy' (singular), one can use 'tu' or 'vous' to express it in French. My argument is that you'd never. IRL, use a polite form of address in the semantics of the situation: any speaker who speaks this particular sentence will be familiar enough with 'my boy' to use 'tu'. So, grammatically, one can use 'tu' or 'vous', but since the object is singular in the example, you cannot pluralize /boy/ into /boy's'/. Practically, though, I doubt one would ever use polite-vous in this context.
Subject-Verb agreement: Je suis, Tu es, Il/Elle/On est, Nous sommes, Vous êtes (not 'étres'), Ils/Elles sont.