This is a question that appears in our textbook.
"Let a and b be constants and let y(i) = ax(i) + b for i = 1, 2, ..., n. What is the relationship between Var(X) and Var(Y)?"
We have then that Var(Y) = a^2(Var(X)) by the simple proof that can be done after factoring out the a's from the formula using sum of x(i)^2 and (sum of x(i))^2
Does this apply to any case where we are able to calculate Var(X) and a is known (even if b is unknown other than the fact that it is a constant)? Does the b in absolutely no way affect variance? (I understand this from a logical and applied perspective, but is it something set in stone that we can use as given?)