Question

3Which table has a constant of proportionality between y and 3 of - ?4it’s 20 points

Answer 1

The constant of proportionality (COP) between y and x is the ratio between the two numbers.

`\text{COP =}(y)/(x)`

Now, we need this ratio to be (3/4). In other words, we want

`(y)/(x)=(3)/(4)`

Now, let us take the first table and see what the ratio (y/x) is.

For the first entry in the first table

`(y)/(x)=(6)/(8)=(3)/(4)`

Which is exactly the ratio (3/4) which we wanted! But let's go to the second entry in the table just to verify if the ratio holds across all numbers.

For the second entry in the first table:

`(27)/(4)*((1)/(9))=(3)/(4)`

Hence it is verified that the first table (choice A) has the ratio of (3/4) between y and x.

The second table does not have a ratio of (3/4) because

`(y)/(x)=(3)/(4)*((1)/(3))=(1)/(4)`

which is not our desired ratio of (3/4).