Which graph represents a linear function?

None of those are linear functions.

Partial quotients is a method of dividing larger numbers by finding smaller, easier multiples of the divisor that are smaller than the dividend, and putting the number needed to multiply the divisor by to get that multiple off to the side. After repeating this process, you add the numbers on the side to get a final answer. For example, if you are dividing 480 by 32, an easy multiple of 32 that is smaller than 480 is 320. To get this, multiply 32 by 10, and put 10 to the side. Then do the standard subtraction to get 160. Then, begin to think about easy multiples of 32 that are less than 160.
96 automatically comes to mind (32 x 3), so put 3 to the side and subtract to get 64. Obviously, 32 goes into 64 twice, so put 2 to the side and subtract to get zero. At this point, all you must do is add all of the numbers on the side:
10 + 3 + 2 = 15 
The answer to 480/32 is 15. To check this, simply use a calculator. This is how you do partial quotients. For further explanation, try this:
http://everydaymath.uchicago.edu/teaching-topics/computation/div-part-quot/
Hope this helps!
~ArchimedesEleven