Identifying proportional & non-proportional functions | Grade 8 (TX TEKS) | Khan Academy

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, where one of the variables, Y, is just equal to some constant times the other variable. So let's see which of these can be written in this way.

Another way of thinking about it is the ratio of Y over X. If you divide both sides by X, it's going to be a constant. So the first one is the distance a train travels in X hours at a constant rate of 80 km per hour.

Let's think about it this way: if we say Y is the distance, well this is, and you're traveling for X hours, you multiply the time times the rate, times 80, and you'll get the distance. If I wrote the units out, they would all work out. So this is in that form: Y is equal to a constant time X. So 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 have been proportional, but because of that service charge, we can see that it's not in this form. So we do not like this one.

The total mass of X identical bricks, each weighing 2.5 kg. So the total mass is just going to be 2.5 times the number of bricks. Once again, Y is equal to a constant time X. So I like this choice as well.

Let's do another example. So here we're told the table represents the cost of renting a paddle board at three rental businesses near a lake. Label each table as a proportional or non-proportional relationship.

All right, remember, a proportional relationship is Y is equal to K * X, or we could say the ratio between Y and X is always going to be a constant. And 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. So here it's 14/1; here it's 20/2. Let me just write that out: 14 over 1, which is, of course, 14. Here it's 20 over 2, which is equal to 10.

Well, I can already see that Y / X is not a constant; this first X and Y, the ratio is 14. The 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: 7/1, so let me write Y over X. 7/1 is 7; 21 divided by 3 is 7; 28 divided by 4 is 7. This one is proportional.

Let's do this one, keep doing Y divided by X. 15 divided by 1 is 15; 20 divided by 2 is 10; 35 divided by 5 is 7—definitely not proportional. So only Paddle Paddle Pro is proportional.