1/ equation of a line : y=ax+b, where a is the slope
2/ if a line passes through 2 points, then the coordinates of these two points satisfy the equation of the line.
Is it enough ?
3/ To prove that 3 points lie on the same line, it is sufficient to prove that the line between 1st and 2nd point and the one between 2nd and 3rd (or 1st and 3rd) have same slope.
Is it enough again ?