Is there a cubic singular at 9 general points

Question

Let $M$ be a collection of $9$ general points in projective 2-dimensional space. Can I then choose a cubic $C$ that is singular at every point of $M$?
I just read this in a book about algebraic geometry (in the context of Bezouts theorem) where it just says 'let $C$ be the cubic singular at every point of $M$'. Why can I choose such a cubic? I've seen this a couple times now that we are just allowed to choose a curve through some points. An other example was a conic being chosen through $4$ double points and one more arbitrary point. In either situation I don't see why such a curve does exist.