The student is wrong because the test he 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 yx. 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" ≠ 4 ≠ 2.5, we can deduce that this function is not a direct variation.