Respuesta :
Answer:
The correct option is C.
Step-by-step explanation:
The proportional relationship between x and y is defined as
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
Where, k is constant of proportion.
In option A, the rate of change is constant because the value of y increased by 4 as the value of x increased by 1.
If a line passing through two points, then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The equation of a line
[tex]y-4=\frac{8-4}{1-0}(x-0)[/tex]
[tex]y=4x+4[/tex]
It is not in the form of [tex]y=kx[/tex]. So, option A is incorrect.
In option B, the rate of change is not constant because the value of y is not increasing by a constant rate the value of x increasing by 1. So, option B is incorrect.
In option C, the rate of change is constant because the value of y increased by 4 as the value of x increased by 1.
The equation of a line
[tex]y-4=\frac{8-4}{2-1}(x-1)[/tex]
[tex]y=4x[/tex]
It is in the form of [tex]y=kx[/tex]. So, option C is correct.
In option D, the rate of change is not constant because the value of y is not increasing by a constant rate the value of x increasing by 1. So, option D is incorrect.
