Erdős Problem 960

### What is the conjecture

https://www.erdosproblems.com/960

Let $r,k\geq 2$ be fixed. Let $A\subset \mathbb{R}^2$ be a set of $n$ points with no $k$ points on a line. Determine the threshold $f_{r,k}(n)$ such that if there are at least $f_{r,k}(n)$ many ordinary lines (lines containing exactly two points) then there is a set $A'\subseteq A$ of $r$ points such that all $\binom{r}{2}$ many lines determined by $A'$ are ordinary.

Is it true that $f_{r,k}(n)=o(n^2)$, or perhaps even $\ll n$?

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

Start with the linked Erdős Problems 960 statement as the specification, then inspect existing formalized conjectures in this repository to find the expected structure and entry point. Done means adding a Lean formalization of the stated conjecture and confirming it fits the repository's conventions.

Written by the indexing model from the issue text.