Identifying proportional & non-proportional functions

0:00- [Narrator] We're asked which situations represent a proportional relationship. Choose all answers that apply. Pause this video and have a go at this before we do this together. All right, before I even look at these choices, a proportional relationship would be between two variables, say X and Y, would be where one of the variables, Y, is just equal to some constant times the other variable.

0:22So let's see which of these can be written in this way. Or another way of thinking about it is the ratio of Y over X, if you divide both sides by X, is going to be a constant. So the first one is the distance of train travels in X hours at a constant rate of 80 kilometers per hour.

0:40Well, let's think about it like this, if we say Y is the distance, well, this is, and you're traveling for X hours, you multiply that, the time, times the rate, times 80, and you'll go get the distance. If I wrote the units out, the units would all work out. So this is in that form. Y is equal to a constant times X.

1:00So I like this one. The total cost of buying X concert tickets at $50 each, plus a $10 service charge. So here, the total cost is going to be the number of tickets times $50, because it's $50 each, but plus a $10 service charge. If there was no service charge, this would've been proportional, but because of that service charge, we can see that it's not in this form.

1:25So we do not like this one. The total mass of X identical bricks, each weighing 2.5 kilograms. So the total mass is just gonna be 2.5 times the number of bricks. Once again, Y is equal to a constant times X. So I like this choice as well. Let's do another example.

1:44So here, we're told the table represents the cost of renting a paddleboard at three rental businesses near a lake. Label each table as a proportional or non-proportional relationship. All right, remember, proportional relationship is Y is equal to K times X, or we could say the ratio between Y and X is always going to be a constant.

2:05And I'll actually use this. This is actually a very useful way of testing proportionality. So here, if we say for all of these, let's say that the time variable is X and the cost variable is Y. Well, let's think about what the ratio of Y over X is. Let me just write Y over X.

2:23So here, it's 14, 14 divided by one. Here it's 20 over two. Actually, let me just write that out. 14 over one, which is, of course, 14. Here, it's 20 over two, which is equal to 10. Well, I can already see that Y divided by X is not a constant. This first X and Y, the ratio is 14.

2:46The second X and Y, the ratio is 10. So this one is not proportional. I don't even have to look at the next one. All right, let's look over here, Y over X, seven divided by one. So let me write Y over X, seven divided by one is seven. 21 divided by three is seven.

3:0428 divided by four is seven. This one is proportional. Let's do this one. Keep doing Y divided by X. 15 divided by one is 15, 20 divided by two is 10, 35 divided five is seven. Definitely not proportional. So only Paddle Pro is proportional.