John thinks that any two lines must have a point of intersection. is he correct? if so how do you know. if not, produce a counterexample.

This isn't necessarily true. When two lines have equivalent slopes, then they are parallel and will never intersect. 

y=1/2x + 12
y=1/2x + -2
These lines can't intersect because there are equal slopes.

However, if the workers do outside of what's normally expected, go ahead and tip.