Question

1) For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.​

Answer 1

Yes, "y" varies directly with "x".

The equation is:
`y=1.375x`

Explanation:

By definition, Direct variation equations have the following form:

`y=kx`

Where "k" is the Constant of variation.

If you solve for "k", the equation is:

`k=(y)/(x)`

Then, given the table provided in the exercise, you can know if "y" varies directly with "x" by finding the quotient of the correspoding values of "x" and "y":

- Dividing
`y=11` by
`x=8` you get:

`(11)/(8)=1.375`

- Divide
`y=22` by
`x=16`:

`(22)/(16)=1.375`

- Dividing
`y=33` by
`x=24`:

`(33)/(24)=1.375`

Since the quotient is constant, then "y" varies directly with "x" and the the Constant of variation is:

`k=1.375`

Therefore, the equation for the Direct variation is:

`y=1.375x`