Determining whether points are collinear $(1,1)(3,9)(6,21)$
The way I figured that this should be solved is by finding the slope of: 
$(1,1)(3,9)$ 
Then, $(3,9)(6,21)$
Finally $(1,1)(6,21)$ 
Which are 4, 4,and 4 respectively. 
So I assume that they are collinear.
Am I correct? And if not, please provide me with an explanation as to what needs to be done to find the answer rather than a direct answer. 

Yes, you are correct. It is sufficient to calculate only two slopes to decide that three points are collinear.
