Question

Which table does not show a direct variation?

Answer 1

Table J

Explanation:

A direct variation is a simple relationship between x and y.

When you are looking for the direct relationship you should use the formula for it y=kx, or you could just divide y over x (
`(y)/(x)`).

Analysing Table F:

The relationship between x and y is 4.

`(-8)/(-1)=4\\\\(-4)/(-1)=4\\\\(0)/(0)= origin\\\\(4)/(1)=4`

The origin is fine and doesn't ruin the relationship.

Analysing Table G:

The relationship between x and y is 5.

`(5)/(1)=5\\\\(10)/(2)=5\\\\(15)/(3)=5\\\\(20)/(4)=5`

Analysing Table H:

The relationship between x and y is
`(1)/(3)`.

`(0)/(0)=origin\\\\(1)/(3)=(1)/(3)\\\\(2)/(6)=(1)/(3)\\\\(3)/(9)=(1)/(3)`

Like I said before the origin doesn't ruin the relationship so it's fine.

Analysing Table J:

This one doesn't have a direct relationship between x and y.

`(1)/(1)=1\\\\(4)/(2)=2\\\\(9)/(3)=3\\\\(16)/(4)=4`