That said, you should have axioms somewhat like these.
Axiom: There are three non-collinear points.
Axiom: Given two points there is a line containing the points.
So you could say something like this.
Given a point P, by the first axiom there is another point Q.
By the second axiom there is a line .
Again by the first axiom . Why is that true?
So . Why is that true?
Can you find a second line .