Answer:
Table 2 and 3 represent a proportional relationship because the ratio between two variables are equivalent.
Step-by-step explanation:
If variable y is proportional to variable x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
[tex]\frac{y}{x}=k[/tex]
where k is constant of proportionality.
For table 1,
[tex]\dfrac{y_1}{x_1}=\dfrac{5}{1}[/tex]
[tex]\dfrac{y_2}{x_2}=\dfrac{9}{2}[/tex]
[tex]\dfrac{5}{1}\neq \dfrac{9}{2}[/tex]
Therefore, table 1 does not represents a proportional relationship.
Similarly
For table 2,
[tex]\dfrac{\frac{7}{2}}{1}=\dfrac{\frac{21}{2}}{3}=\dfrac{\frac{35}{2}}{5}=\dfrac{\frac{49}{2}}{7}=\dfrac{\frac{63}{2}}{9}=\frac{7}{2}[/tex]
All ratios are equivalent, therefore Table 2 represents a proportional relationship.
For table 3,
[tex]\dfrac{110}{2}=\dfrac{275}{5}=\dfrac{495}{9}=\dfrac{770}{14}=55[/tex]
All ratios are equivalent, therefore Table 3 represents a proportional relationship.
For table 4,
[tex]\dfrac{29.25}{3}=\dfrac{48.75}{5}\neq \dfrac{74}{8}[/tex]
All ratios are not equivalent, therefore Table 4 does not represent a proportional relationship.
