Injective function
Proof: Let xo and x1 be real numbers. Suppose the line maps these two x-values to the same y-value.  This means a·xo+b=a·x1+b. Subtract b from both sides. We get a·xo=a·x1. Now divide both sides by a (remember a≠0).  We get xo=x1. So we have proved the formal definition and the function y=ax+b where a≠0 is an injection.