Comparing constants of proportionality graphically

0:00- [Narrator] Clark has a budget of $12 to spend to buy nuts for his party. The three lines represent the cost of buying bags of three kinds of nuts by varying weights. Which kind of nut can Clark buy the most of with his $12 budget? So pause this video and have a go at that.

0:17Okay. So Clark has a $12 budget. Let's see how we would represent that here graphically. So that's the cost and we want to max the cost at 12. So let's see, this is one, two, three, four, five, six, seven, eight, nine, 10, 11, 12. So if this graph kept going up vertically, it would be there.

0:38And actually just for the sake of it, let me, let me keep this line going all the way up. And let's say that this right over here is $12, our cost in dollars. And so we could have a dotted line over here. And if you just extended each of these lines further out, this is the walnut line, this is the pecan line, this is the peanuts line.

1:00We just have to say, which one can you buy the most of with the $12 budget? And you can see, you don't have to be exactly, we don't have to get exactly where we hit there, although we could calculate that in a second. We can see that you're getting the most kilograms.

1:14You're going furthest out to the right with the peanuts. So the answer to the question would be peanuts. Another way that you could try to do this is you could try to establish the equation for each of these. You could see that at least for walnuts, we can see you can get, you pay $5 for every 0.5 walnuts.

1:38So if you were to take, if you were to take the cost, and you were to divide it by the walnuts, you would get, it would be five divided by 0.5, five divided by 0.5, which is the same thing as 10. Or another way to think about it is the cost of the walnuts or the dollars going to be equal to 10 times the number of walnuts.

2:00Constant proportionality is 10. You could view that as $10 per kilogram of walnuts. You could do the same thing with pecans. Let me find a location right over here. It looks like for every kilogram, we're spending $8. So pecans are going to be having a constant proportionality of eight.

2:19So that's for the pecans. And so it's $8 per kilogram, so it's a little bit cheaper. And then the peanuts, it looks like you can get, it looks like you can do $4 per kilogram. One kilogram is $4. Two kilograms is $8. So maybe I should call this pecans because I have to use a P.

2:40Whoops, what am I doing here? So the cost, so the cost is equal to $8, times...I'll write pec for pecans, and the cost is equal to, we just said $4 per peanut. And so once again, another way to think about it is the cost per kilogram of peanuts is the least so you can buy the most bags.

3:04You can actually buy three kilograms of peanuts if you were to put a 12 right over here, and solve for peanuts. That's where we are right over here, three kilograms. Anyway, we answered this question in multiple ways.