Work Step by Step
Let $f(x)=ax+b, g(x)=cx+d$ be two linear functions. Then, if $f(0) = g(0)$, we get that $b=d$, and moreover if $f(1) = g(1)$, we get that $a+b=c+d$; that is, $a=c$. Hence, the functions $f, g$ are identical; i.e. $f=g$.