Writing proportional equations

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 Iran's 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 and 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 has to 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 eight point five eight point five 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 eight point five times H eight point five times H and we're done if we wanted to write their units we could write D is equal to eight point five kilometers per hour times H which is given in hours