Assuming that the equation of your line is of the form y = mx + c.
The equation can now be rewritten as y - mx - c = 0.
Let's assume that the co-ordinates of the points are - (x1,y1), (x2,y2),..., (xi,yi), so putting (x1,y1) in y - mx - c, we get
a = y1 - mx1 - c
And a can be greater than 0, or less than 0.
For the points above the line, a would be greater than 0, and for the points below the line, a would be less than 0; or could be vice-versa (depending on m and c).
This is how you could determine whether the points fall below/above the line.