0: 0
3: 1
6: 2
9; 3
is this direct variation or not?

Yes, the table represent a direct variation

Step-by-step explanation:

we know that

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

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

In this problem , if the table represent a linear function, then the table represent a direct variation

Verify

For x=3, y=1

Find the value of the constant k of proportionality

 ---->

For x=6, y=2

Find the value of the constant k of proportionality

 ---->

For x=9, y=3

Find the value of the constant k of proportionality

 ---->

The values of k are equal

therefore

The table represent a direct variation

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !