Answer:
Option D. [tex]y=2x+2[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Verify each case
case A) we have
[tex]y=-2x[/tex]
Is a equation of the form [tex]y=kx[/tex]
The value of k=-2
This equation represent a proportional relationship
case B) we have
[tex]y=2x[/tex]
Is a equation of the form [tex]y=kx[/tex]
The value of k=2
This equation represent a proportional relationship
case C) we have
[tex]y=-2x+0[/tex]
The line passes through the origin, because the y-intercept is b=0
This equation represent a proportional relationship
case D) we have
[tex]y=2x+2[/tex]
The line not passes through the origin, because the y-intercept is not equal to zero (b=2)
This equation not represent a proportional relationship
