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