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? 

any point, y, on line in 2d cartesian space can satisfy following equation:
y = a*x + b, where a and b are constant real numbers, and x is real number with range (-inf, +inf)
because x has infinite range, so y has inf range.
this prove line has infinite number of points
