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
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is constant of proportionality.
We know that, proportional relationship passes through the origin because (0,0) satisfy [tex]y=kx[/tex].
For x=0, check which equation has y=0.
In option A, [tex]y=-3(0)-2=-2[/tex].
In option B, [tex]y=9[/tex].
In option C, [tex]y=4(0)=0[/tex].
In option D, [tex]y=3(0)+1=1[/tex]
Only in option C, we have a equation of the form [tex]y=kx[/tex] with 4 as constant of proportionality and it passes through (0,0).
Therefore, the correct option is C.
