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

Answer:

The correct option is C.

Step-by-step 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

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of a line

$y-4=\frac{8-4}{1-0}(x-0)$

$y=4x+4$

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

$y-4=\frac{8-4}{2-1}(x-1)$

$y=4x$

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.