3-Approximation for General position subset
Find any line containing $\geq 3$ points. Delete all points on this line. Repeat.

This is a $3$-approximation, since on any line containing $m\geq 3$ points we must delete at least $m-2\geq 1$ points and we delete at most $2$ points too many. Meanwhile, the objective value decreases by at least $m-2\geq 1$.

If we know that the true objective value is $K$, then the instance obtained by deleting all points on this line will have objective value $\leq K-(m-2)$ and thus the recursive application will, by induction, return a solution removing at most $3(K-(m-2))$ points. Thus, we remove at most $3(K-(m-2))+m=3K-2m+6\leq 3K$ points.