Question

Which explains whether or not the function represents a direct variation?

Answer 1

Answer:b

Explanation:

Answer 2

The function represents a direct variation

Explanation:

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`

In a linear direct variation the line passes through the origin and the constant of proportionality k is equal to the slope m

Let

`A(0,0)` ------> the line passes through the origin

`B(2,10)`

Find the value of k------> substitute the value of x and y

`y/x=k`----->
`k=10/2=5`

`C(4,20)`

Find the value of k------> substitute the value of x and y

`y/x=k`----->
`k=20/4=5`

`D(6,30)`

Find the value of k------> substitute the value of x and y

`y/x=k`----->
`k=30/6=5`

`E(8,40)`

Find the value of k------> substitute the value of x and y

`y/x=k`----->
`k=40/8=5`

The value of k is equal in all the points of the table and the line passes through the origin

therefore

The function represents a direct variation

the equation of the direct variation is equal to

`f(x)=5x`