Question

PLEASE HELP ASAP!!!

Does the table shown represent a direct variation? If so, what is the equation?
x-values:0,2,4 and y-values:0,4,8
A. No
B. Yes; y=2x-2
C. Yes; y=2x
D. Cannot be determined

Answer 1

Option C. Yes; y=2x

Explanation:

we know that

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

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

so

In this problem

For x=0, y=0

That means ----> the line passes through the origin

Find the value of k

For x=2, y=4

`k=(y)/(x)` ---->
`k=(4)/(2)=2`

For x=4, y=8

`k=(y)/(x)` ---->
`k=(8)/(4)=2`

The values of k are equal

therefore

The table represent a direct variation

The equation is equal to

`y=2x`