Three points are collinear if they lie on the same line. To check this, compute the slope between the first two points and the slope between the second and third points. If the slopes match, the points are collinear.
Points (1, 2), (2, 4), and (3, 6) are collinear. Slope from (1,2) to (2,4) is (4-2)/(2-1) = 2. Slope from (2,4) to (3,6) is (6-4)/(3-2) = 2. Same slope means same line.
You can also use the area method: if the area of the triangle formed by the three points is zero, they are collinear.