Erdős Problem 588

### What is the conjecture

https://www.erdosproblems.com/588

Let $f_k(n)$ be minimal such that if $n$ points in $\mathbb{R}^2$ have no $k+1$ points on a line then there must be at most $f_k(n)$ many lines containing at least $k$ points. Is it true that
$$f_k(n)=o(n^2)$$
for $k\geq 4$?

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

No files, tests, or entry points are mentioned. Start by reading the linked Erdős Problems page and the repository's existing formalizations of similar geometric conjectures. Done means adding a Lean formalization of the stated conjecture that fits the project's conventions and passes the relevant project checks.

Written by the indexing model from the issue text.