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 4|28 6| 48| 8| 72

A. yes; y = 2x
B. yes; y = 5x
C. yes; y = 7x
D. no; y does not vary directly with x

Answer 1

Let's have a look:

2(4)= 8 (this would not work)

5(4)= 20 (this wouldn't work)

7(4)= 28 This does, let's check the others.

7(6)= 42 This does not work.

"D" would be the correct answer.

I hope this helps!
~cupcake

Answer 2

The answers is D.

Explanation:

That
`y` varies directly with
`x` means that there exist a constant
`k` such that
`y = kx`. If we suppose that
`y` varies directly with
`x` , then

`4k = 28` ,
`6k = 48` and
`8k = 72`,

from where we get

`k = (28)/(4)`,
`k = (48)/(6)` and
`k = (72)/(8)`

and hence

`k = 7`,
`k = 8` and
`k = 9`.

Since the value of
`k` is not constant, then
`y` does not vary directly with
`x`.