Given:
There exist a proportional relationship between x and y.
To find:
The equation which represents a proportional relationship between x and y.
Solution:
If there exist a proportional relationship between x and y, then


where, k is constant of proportionality.
We know that, proportional relationship passes through the origin because (0,0) satisfy
.
For x=0, check which equation has y=0.
In option A,
.
In option B,
.
In option C,
.
In option D, 
Only in option C, we have a equation of the form
with 4 as constant of proportionality and it passes through (0,0).
Therefore, the correct option is C.