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