You want a linear function f(x) such that f(a)=A and f(b)=B given a, b, A, B. A valid f(x) (actually it's the only one) is defined as x-b x-a

You want a linear function f(x) such that f(a)=A and f(b)=B given a, b, A, B. A valid f(x) (actually it's the only one) is defined as x-b x-a f(x) = A --- + B --- a-b b-a You can calculate f(a) and f(b) to confirm that it works. However, I don't find this kind of guide any good for learning math...