Constant of proportionality from tables

- [Instructor] We are asked, Which table has a constant of proportionality between y and x of 0.6? Pause this video and see if you can figure that out. All right, so just as a reminder, the constant of proportionality between y and x, one way to think about it is that y is equal to some constant times x. Y is proportional to x. And this constant right over here is our constant of proportionality. So if that's going to be 0.6, so in our tables, or in the table that has a constant of proportionality of 0.6, y should be equal to 0.6 times x for every x,y pair. So let's look at these choices. So is seven 0.6 times four? Well, no, seven is larger than four. 0.6 times four would actually be 2.4, so this one is not gonna be, is definitely not going to have a constant of proportionality of 0.6. And in fact, this table, this isn't even a proportional relationship. For this first one, I would have to multiply by 7/4. And then here I'm going to be multiplying by 10/6, which is equivalent to 5/3. And here I'm multiplying by 13/8, so I'm not multiplying by the same constant every time. So this isn't even a proportional relationship. Now let's look at choice B. Well, to go from four to 2.4, that is. You would multiply by 0.6. But that's not enough for us to say that this is truly a proportional relationship. It would have to be 0.6 in every scenario. So let's see. Nine times 0.6, yeah, that is 5.4. Nine times six is 54. But now this is nine times 6/10. It's 54 divided by 10, which is 5.4. And now let's see, 14 times six is 84. So 14 times 6/10 would indeed be 8.4. So this looks like our choice. And we can verify that this would not be the case. Let's see, three, to get to two we would be multiplying by 2/3. And then here, once again, we're multiplying by 2/3. And then here, once again, we're multiplying by 2/3. So this is actually describing a proportional relationship, but our constant of proportionality here is 2/3, which, if you tried to express it as a decimal, it would be 0.6 repeating. 2/3 is equal to 0.6 repeating. And so it is proportional but does not have this constant of proportionality. So we like our choice B.