Determining if 2 points lie on the same line

Question

How to determine if points lie on the same line, given an equation and 2 points. Example:y=2x + 4. (7,20)

Answer 1

If you have an equation for the line then any point you are given must satisfy the equation.

In the example y=2x+4, we put in the given x coord (x=7) and see what y value the equation produces.

y=2×7+4=14+4=18. The equation produces y=18, but the y coord is 20, so the equation is not satisfied therefore the point (7,20) does not lie on the line. The point (7,18) does lie on the line.