Question

How do you determine whether three sets of points is collinear

Answer 1

Step 1) Write an equation of the line determined by two of the points.

Unless the y-intercept is too hard to find, we're probably going to use slope-intercept form to accomplish this.
Slope-intercept form is written as $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x = 0)

Step 1a) We find the slope with the change in the y-coordinates of the two points (the "rise") over the change in the x-coordinates. (the "run")

Step 1b) We can use this slope to find the y-intercept, the value of y when x = 0.
We know how y changes accordinate to changes in x by the slope.
Just take one of the points of our line, see how much x needs to change to become equal to 0, and change y accordingly.

Step 2) We can take our third point and plug in its x and y values in that equation, now that we have the equation of our line filled out. If you evaluate the equation and it is true, then the point is on that line. If it's not true for those values, the point is not on the line.

Answer 2

I think you mean "a set of three points". What I would do is take one point, find the slope from that point to another one, and then find the slope from the same starting point to the third one. If the (absolute values of the) slopes from the same starting point to each of the others are equal, then the three points are collinear.