Given:
Four equations in the options.
To find:
The equation which represents a proportional relationship.
Solution:
If y is proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is the constant of proportionality.
In this case if x=0, then y=0. It means the graph of a proportional relationship passes through the origin.
From the given options, only option B, i.e., [tex]y=\dfrac{1}{4}x[/tex], is of the [tex]y=kx[/tex], where, [tex]k=\dfrac{1}{4}[/tex].
So, the equation [tex]y=\dfrac{1}{4}x[/tex] represents a proportional relationship.
Therefore, the correct option is B.
