Respuesta :

Answer:

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 [tex]y/x=k[/tex] or [tex]y=kx[/tex]

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

[tex]k=y/x[/tex]  ----> [tex]k=1/3[/tex]

For x=6, y=2

Find the value of the constant k of proportionality

[tex]k=y/x[/tex]  ----> [tex]k=2/6=1/3[/tex]

For x=9, y=3

Find the value of the constant k of proportionality

[tex]k=y/x[/tex]  ----> [tex]k=3/9=1/3[/tex]

The values of k are equal

therefore

The table represent a direct variation

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