ANSWER
Yes, this relationship is proportional
EXPLANATION
A proportional relationship has the equation:
[tex]y=kx[/tex]where k is called constant of proportionality.
To see if this relationship is proportional first we have to find k:
[tex]k=\frac{y}{x}[/tex]This constant, as the name itself describes, must be constant. This means that for each pair from the table we have to find the same number if we divide the y-value by the x-value.
For the first pair:
[tex]k=\frac{3}{2}[/tex]Second pair:
[tex]k=\frac{4}{6}=\frac{2}{3}[/tex]Note that we can simplify the fractions to get an equivalent one.
Third pair:
[tex]k=\frac{6}{9}=\frac{2}{3}[/tex]Fourth pair:
[tex]k=\frac{8}{12}=\frac{2}{3}[/tex]Fifth pair:
[tex]k=\frac{10}{15}=\frac{2}{3}[/tex]For each pair from the table we got the same constant. Therefore, this relationship is proportional.
