Writing proportional equations | Rates & proportional relationships | 7th grade | Khan Academy

We're told that Justin runs at a constant rate, traveling 17 kilometers in two hours. Write an equation that shows the relationship between the distance he runs, ( d ), in kilometers and the time he spends running, ( h ), in hours. So pause this video and see if you can work through that on your own before we do it together.

All right, now there's several ways to approach this question. One way is to say, look, he's running at a constant rate, so his distance is going to be equal to some constant. Let's just call that lowercase ( k ) times the amount of time he spends running. The way that we can figure out what ( k ) is, is by using the information that they gave us. They tell us right over here that when our distance is 17 kilometers—so when our distance is 17 kilometers—that's a situation where he has been running for two hours.

So that is going to be equal to ( k ) times two hours. So what is ( k ) going to be? Pause the video again and see if you can figure it out. If you didn't figure it out the first time I asked you to pause the video…

All right, well, there's a bunch of ways to solve for ( k ), but one way is to say let's just divide both sides by two hours. So if you divide both sides by two hours, you are going to get that ( k ) is going to be equal to ( 17 ) over ( 2 ) kilometers per hour, which is ( 17 ) over ( 2 ) is ( 8.5 ) kilometers per hour.

And so if we go back to the original question, which asks us to write an equation that shows the relationship between ( d ) and ( h ), we can say that ( d ) is equal to… we now know our proportionality constant; it is ( 8.5 ) times ( h ). ( 8.5 ) times ( h ), and we're done.

If we wanted to write their units, we could write ( d ) is equal to ( 8.5 ) kilometers per hour times ( h ), which is given in hours.