Question

Does the following table show a proportional relationship between the variables x and y. x 1/4 2/4 3/4 y 3 6 9

Answer 1

The answer is Yes you are welcome

Answer 2

Yes the table shows a proportional relationship between the variables x and y.

Explanation:

Given : Table

`x : (1)/(4)\ \  (2)/(4)\ \  (3)/(4) \\\\y : 3\ \ \  6\ \ \  9`

To find : Does the following table show a proportional relationship between the variables x and y.

Solution :

The proportional relationship between the variables x and y is given by,

`y=kx`

Where, k is constant of proportionality

We substitute,
`x=(1)/(4)` and y=3

`3=k((1)/(4))`

`k=3* 4`

`k=12`

So, The equation form is
`y=12x`

If rest points satisfy the equation then they are proportional.

Put
`x=(2)/(4)`

`y=12* (2)/(4)`

`y=6`

True.

Put
`x=(3)/(4)`

`y=12* (3)/(4)`

`y=9`

True.

Therefore, Yes the table shows a proportional relationship between the variables x and y.