The following data was collected on a cheetah its ran 1/2 mile in 2/3 min,1/4 in 1/3 min, and 3/4 mike in 1 min. explain how you know this is a proportional relationship

Proportional means equal, by the way.

I know that this is a proportional relationship because, if you really look at it, you can see the equality between the three pieces of data. 1/2 = 2/4, and 2/4 mile in 2/3 minute... Divide those two numerators by 2/2 and you get the next data piece. Now, multiply the second data piece by 3/3, and you get the third piece.

Now, look at the numbers I told you to multiply/divide by. They all equal 1. In other words, the only difference between them is the time, the unit rate of the distance (1/4 mile/1/3 min) remains the same.

Definitely