Constant of proportionality from tables | 7th grade | Khan Academy

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, 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 xy 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 definitely not going to have a constant of proportionality of 0.6. In fact, this table, this isn't even a proportional relationship, where for this first one I would have to multiply by seven-fourths, and then here I'm going to be multiplying by ten-sixths, which is equivalent to... and here I'm multiplying by 13 over eight. 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 4 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, 9 times 0.6... yeah, that is 5.4. 9 times 6 is 54, but now this is 9 times 6 tenths; it's 54 divided by 10, which is 5.4.

And let's see, 14 times 6 is 84, so 14 times 6 tenths 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, 3 to get to 2, we would be multiplying by two-thirds, and then here once again we're multiplying by two-thirds, and then here once again we're multiplying by two-thirds. So this is actually describing a proportional relationship, but our constant of proportionality here is two-thirds, which if you try to express it as a decimal would be 0.6 repeating. Two-thirds 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.