Answer
The student is wrong because the test he is performed is incorrect.
Work Step by Step
The student makes an error because it does not matter how each x coordinate increases and how each y coordinate increases. What matters is the ration of $\frac{y}{x}$. If that ration is constant for each x-coordinate and its respective y-coordinate, then we can deduce that the function is a direct variation.
In this scenario, lets use this test to see if the rations are constant:
3/0=undefined
4/1=4
5/2=2.5
Since, "undefined" $\ne$ 4 $\ne$ 2.5, we can deduce that this function is not a direct variation.
