Let:
x = Number of insects
y(x) = Number of butterflies
k = constant of proportionality
She noticed that 4 out of every 15 flying insects she saw at the park were butterflies, therefore:
[tex]\begin{gathered} y(x)=k\cdot x \\ x=15 \\ y(x)=4 \\ 4=k\cdot15 \\ \text{Solving for k:} \\ k=\frac{4}{15} \end{gathered}[/tex]
Therefore, the function which represents this situation is:
[tex]y(x)=\frac{4}{15}x[/tex]
