How to introduce a natural manifold structure into the set of all straight lines?
I have a set X which is the set of all straight lines in R^2.
These lines are not necessarily through the origin.
I am unsure of how to introduce a natural manifold structure into this set X.
I know i need to write down charts showing the domains and codomains but i don't know what the charts are.
I think defining coordinate charts on X requires considering equations that specify straight lines but im not certain.
Thanks for any help