Mapping of line that passes through $a$, $b$ (distinct complex number) using: $z\mapsto \frac{z-a}{z-b} $

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I'd like to determine the image of the line through $a$, $b$ (distinct complex number) using the mapping $z\mapsto \frac{z-a}{z-b} $.

What I did so far:

$a\mapsto 0$, and: $b\mapsto \infty$

Can I conclude something now?