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## Compare and interpret constants of proportionality

## Video transcript

- [Instructor] We can
calculate the depth d of snow, in centimeters, that
accumulates in Harper's yard during the first h hours of a snowstorm using the equation d is
equal to five times h. So d is the depth of snow in centimeters, h is time that elapses in hours. How many hours does it take
for one centimeter of snow to accumulate in Harper's yard? Pause this video and see
if you can figure that out. All right so we wanna figure out what h gives us a d of one centimeter. Remember d is measured in centimeters. So we really just need
to solve the equation one centimeter, when d is equal to one, what is h going to be? And to solve for h we just need to divide both sides by five. So you divide both sides by five, the coefficient on the h, and you are left with h is equal to 1/5. And the unit for h is hours, 1/5 of an hour. So 1/5 of an hour. If they had minutes there, then you would say well 1/5 of an hour, there's 60 minutes,
well this is 12 minutes. But they just want it
as a number of hours, so 1/5 of an hour. How many centimeters of snow accumulates in per hour? Or this is a little bit of a typo. How many centimeters of snow accumulate in we could say one hour, in one hour, or they could have said how many centimeters of
snow accumulate per hour. That's another way of thinking about it. So we could get rid of per hour. So pause the video and see
if you can figure that out. Well there's a couple of
ways to think about it. Perhaps the easiest one is to say, well what is d when h is equal to one? And so we could just say d when h is equal to one, when only one hour has elapsed, well it's going to be five times one which is equal to five, and our units for d are in centimeters. So five centimeters. Let's do another example. Betty's Bakery calculates
the total price d in dollars for c cupcakes using the equation d is equal to two c. What does two mean in this situation? So pause this video and see if
you can answer this question. So remember d is in
dollars for c cupcakes. Now one way to think about it is, what happens if we take d
is equal to two times c, what happens if we divide both sides by c? You have d over c is equal to two. And so what would be the
units right over here? Well we have dollars, d dollars, over c cupcakes. So this would be $2, because that's the units
for d, per cupcake, dollars per cupcake. This is the unit rate per cupcake. How much do you have to pay per cupcake? So which of these
choices match up to that? The bakery charges $2 for each cupcake, yeah $2 per cupcake, that looks right. The bakery sells two
cupcakes for a dollar. No that would be two cupcakes per dollar, not $2 per cupcake. The bakery sells two types of cupcakes. No no we're definitely not
talking about two types of cupcakes, they're just
talking about cupcakes generally, or I guess one type of
cupcake, we don't know, but just cupcakes generally
is $2 per cupcake.