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Interpreting graphs of proportional relationships

Worked example interpreting graphs of proportional relationships.

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Video transcript

- [Instructor] We are told the proportional relationship between the number of hours a business operates and its total cost of electricity is shown in the following graph, all right. Which statements about the graph are true? Choose all answers that apply. So pause this video and see if you can figure this out. All right, now let's do this together. And before I even look at the choices, let me analyze this a little bit. It is a proportional relationship. So we know that our total cost, let me write it here. Our total cost is going to be equal to some constant of proportionality times our number of hours. And we can even figure out what that constant of proportionality is going to be, because they give us this point A. We know that when our hours are four, so when this is four right over here, our total cost is $120. $120. So what times four is equal to 120? Well, we know that this k must be 30, 'cause 30 times four is 120. So we can write that proportional relationship where our total cost is going to be equal to our constant of proportionality, 30, times our number of hours. Number of hours. So let's see which of these choices, and it might be more than one, say this or describe what's going on here. So choice A, the y-coordinate of point A, so point A is at the point four comma 120, so the y-coordinate is the 120. That's the total cost when you run your business for four hours. The y-coordinate of point A represents the total cost of electricity when the business operates for four hours. Yes, that is exactly or very close (laughs) to what I just said, so I like this one. The total cost of electricity is $35 when operating the business for one hour. So let's go to one hour here. This is going to be the total cost. Now, you might say, hey, this looks kinda close to $35, but that's why it was useful for us to write this relationship right over here, because what we see is that our total cost is going to be 30 times our number of hours. Our total cost here is actually going to be 30, not 35. And it actually does look smack dab in between 20 and 40 versus a little bit closer to 40. So this one is not going to be true. And we're not gonna select none of the above, 'cause we actually did select one of the above. And we're done.