To check if a point, such as (1, -1), is on your line, you can either sub in both the x and y values of each point into your line's equation, or one and check if the other matches up with your point.
For example, the x value of (1, -1) is 1, and the y value is -1. Sub these points into your equation:
y = 2x - 3 Original equation
(-1) = 2(1) - 3 Sub in points
-1 = 2 - 3
-1 = -1 Sides equal, therefore point is on line
If a point is NOT on the line:
y = 2x - 3 Original equation
(2) = 2(4) - 3 Sub in points
2 = 8 - 3
2 = 5 Sides do NOT equal, point is NOT on line, NOT a solution