Writing y = mx proportional equations worked example 2
About this video
A craft store sells beads at 12 cents each, and the video finds the equation for the total price P of N beads. By trying 0, 1 and 2 beads (0, 12 and 24 cents) it sees that the price is always 12 times the number of beads, so P = 12N. The unit rate of 12 cents per bead is the slope, and the line goes through the origin, so it is proportional.
You'll be able to
- write an equation like P = 12N from a price per item.
- explain why the unit rate is the slope of the line.
- explain why a proportional relationship passes through the origin.
Key words
- unit rate
- The price or amount for one item, like 12 cents per bead.
- slope
- How much the output goes up when the input goes up by one.
- origin
- The point (0, 0) on a graph.
- proportional relationship
- A relationship where one quantity is always the same number times the other.
Transcript
- [Instructor] We are told a craft store sells beads for making jewelry at a price of 12 cents per bead. Which equation represents the total price, P, to purchase N beads? Pause this video and see if you can think about this on your own. All right, now let's do this together.
So there's a bunch of ways that we could think about it. One is, is that we could think about, well, what is our price going to be for a given number of beads? I guess we're going to use N for beads. So we already know it's 12 cents per bead. So if we have one bead, it's going to be 12 cents.
What if it was zero beads? Well then it's going to be 0 cents. We haven't bought any. What if it's two? Well, then it's going to be 24 cents. So whatever the number of beads are, we're essentially going to be multiplying it by that 12 cents in order to get the price.
We're multiplying by 12 cents, we're multiplying by 12 cents, so let me write that down. The price is going to be equal to whatever the number of beads are, times 12 cents. Or I could also write that as 12 cents times the number of beads. This unit rate that we're giving here, the price per bead, this you could think of as the slope, if we've visualized this at a line.
We could also see this as a proportional relationship, that it goes through the origin when N is equal to zero, P is equal to zero. And every time N increases by one, our price is going to increase by 12 cents. So we just wrote down without even looking at the choices, exactly what we have here for choice D, and we are done.
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