Proportional relationship
Proportional relationships are relationships between two variables where their ratios are equivalent.
Let us select any two options to confirm their proportional relationship
Selecting the first option
The formula for the proportional relationship in the first option is,
[tex]\text{Proportional relationship=}\frac{Total\text{ cost of tickets}}{\text{Number of tickets}}[/tex]
Therefore,
[tex]\begin{gathered} \frac{\text{ \$54}}{2}=\text{ }\frac{\text{\$81}}{3}=\text{ }\frac{\text{\$108}}{4}=\text{ }\frac{\text{\$135}}{5} \\ \text{ \$27=\$27=\$27=\$27} \end{gathered}[/tex]
From the calculation done above, we can conclude that the first option represents a proportional relationship.
Selecting the last option
[tex]\text{Proportional relationship=}\frac{\text{Distance}(mi)}{\text{time(h)}}[/tex]
Therefore,
[tex]\begin{gathered} \frac{80}{2}=\frac{120}{3}=\frac{160}{4}=\frac{200}{5} \\ 40=40=40=40 \end{gathered}[/tex]
From the calculation done above, we can conclude that the last option represents a proportional relationship.
Hence, the correct options are Option 1 and 4.
