I got asked to prove that a function is linear iff it is affine and maps zero to zero, but I have no idea how to start relating the definitions of affine and linear.

AFFINE: f(1-t(u)+tv) = (1-t)f(u) + tf(v)

LINEAR: f(u*v) = f(u) + f(v) AND f(au) = af(u)

What the fuck do I do with the t and 1-t?