Do arity or dimension of relations depend on how many variables are involved?

Question

1) y = x + 1

It seems like even though the above has both "=" and "+", there are only two variables, so the relation would be a binary one, where as...

2) z = x + y

has 3 variables so there is a tertiary relation.

Is this sensible or am I missing someone fundamental?

Answer 1

makes sense. (1) relates 2 quantities but (2) relates 3 different ones...

Answer 2

While $z=x+y$ is a boolean function of three variables, currying $y=1$ gets the two-variable function $z=x+1$. These facts identify such functions' minimal arities (the implementation of them might increase arity with unused arguments, e.g. def f(x, y, z, a): return z==x+y in Python has arity $4$).