Constant of proportionality from tables

we are asked which table has a constant of proportionality between y and X of zero point six pause this video and see if you can figure that out alright 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 XY pair so let's look at these choices so is 7 0.6 times 4 well no 7 is larger that than 4 0.6 times 4 would actually be 2 point 4 so this one is not going to 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 where for this first one I would have to multiply by 7/4 and then here I'm going to be multiplying by 10 sixths which is equivalent to 5/3 and here I'm multiplying by 13 over 8 so I'm not multiplying by the same constant every time so this isn't 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 6/10 it's 54 divided by 10 which is 5 point 4 and let's see 14 times 6 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 3 to get to 2 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 proportion relationship but our constant of proportionality here is 2/3 which if you try to express it as a decimal 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 be