Finding the line containing a point at infinity and a point of the form $(x:y:1)$

Question

How do you find the line containing $(0:0:1)$ and $(1:2:0)$ that does not contain $(1:1:1)?$

I tried to use projective transformation, but I ended up getting the line $\ell(x,y,z)=z$ which I know is wrong since it does not contain $(0:0:1)$.

Please help!