Question

Which table shows a proportional relationship between x and y? A 0,4 1,8 2,12 B 0,0 1,1 2,4 C 1,4 2,8 3,12 D 1,2 2,4 3,8

Answer 1

The correct option is C.

Explanation:

The proportional relationship between x and y is defined as

`y\propto x`

`y=kx`

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

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The equation of a line

`y-4=(8-4)/(1-0)(x-0)`

`y=4x+4`

It is not in the form of
`y=kx`. 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

`y-4=(8-4)/(2-1)(x-1)`

`y=4x`

It is in the form of
`y=kx`. 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.