Question

The following data were collected on a cheetah. It ran 1/2 mile in 2/3 min, 1/4 mile in 1/3 min, and 3/4 mile in 1 min.Explain how you know that this is a proportional relationship?

Answer 1

We want to find why the relationship above shown is proportional.

If we take the distance as a function of time, we have that:

`\begin{gathered} \text{When }t=(2)/(3),d=(1)/(2) \\ \text{When }t=(1)/(3),d=(1)/(4) \\ \text{When }t=1,d=(3)/(4) \end{gathered}`

If we want to see if the relationship is proportional, we have to take the quotients of the distance between the time. If all the quotients are the same, we could say that the relationship is proportional, and that the quotient is the constant of proportionality. Thus, doing the quotients we obtain:

`\begin{gathered} ((1)/(2))/((2)/(3))=(3)/(4),((3)/(4))/(1)=(3)/(4) \\ ((1)/(4))/((1)/(3))=(3)/(4) \end{gathered}`

As all the values are the same, we say that 3/4 is the constant of proportionality, and that the relationship is proportional.