Answer:
D) ![y=-2x](https://tex.z-dn.net/?f=y%3D-2x)
Step-by-step explanation:
A linear relationship is of the form
, where,
is the slope and
is the y-intercept (constant).
For a proportional relationship, the value of
and thus it is of the form
Let us check each option and express it in the form above.
Option A:
![y=2](https://tex.z-dn.net/?f=y%3D2)
This can be written as
. So,
.
Since, b \ne 0, therefore, it is not a proportional relationship.
Option B:
![y=14x+1](https://tex.z-dn.net/?f=y%3D14x%2B1)
Here,
. So,
.
Since, b \ne 0, therefore, it is not a proportional relationship.
Option C:
![y=x-4](https://tex.z-dn.net/?f=y%3Dx-4)
Here,
. So,
.
Since, b \ne 0, therefore, it is not a proportional relationship.
Option D:
![y=-2x](https://tex.z-dn.net/?f=y%3D-2x)
This can be rewritten as ![y=-2x+0](https://tex.z-dn.net/?f=y%3D-2x%2B0)
There is no y-intercept on this. So,
Since,
, therefore, it is a proportional relationship.
Therefore, the correct option is D.