How to prove that a straight line is an infinite set of points? From the basic elementary level when we start reading geometry we get this idea developed in us that a straight line is the conjuction of infinite points.but how to prove this?  I mean is this an axiom or its provable? 

You might know the equation of a straight line through 2 points which is: $$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$$
From that we can see that there are infinite solutions to satisfy this equation which proves that a straight line contains infinite points.
