Question

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

x y
---------------------------
10 12
15 18
20 24

a.) yes; y=1.2x
b.) yes; y=2x
c.) yes; y=x+1
d.) no; y does not vary directly with x.

Answer 1

The correct answer is A.

Answer 2

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form
`y/x=k` or
`y=kx`

Verify

A) For the point
`(10,12)`

Find the value of k

`k=y/x`

substitute

`k=12/10=1.2`

B) For the point
`(15,18)`

Find the value of k

`k=y/x`

substitute

`k=18/15=1.2`

C) For the point
`(20,24)`

Find the value of k

`k=y/x`

substitute

`k=24/20=1.2`

so

The value of k is equal to
`1.2`

The equation of the direct variation is equal to

`y=1.2x`

therefore

the answer is the option a

yes;
`y=1.2x`