Question

In which of the tables below x and y are inversely proportional? Find the constant of variation. If there is one. (a) x:y, 3:8, 4:6, 5:4.8, 5.5:4

(b) x:y, 0.1:300, 0.5:60 75:0.4, 100:0.3

Answer 1

Answer: Only (A)

If you go RSM this the Answer.

Answer 2

The table B represent an inverse variation

The constant of variation k is 30

Explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form
`y*x=k` or
`y=k/x`

Verify table A

For x=3, y=8 ---->
`k=y*x` ---->
`k=8*3=24`

For x=4, y=6 ---->
`k=y*x` ---->
`k=6*4=24`

For x=5, y=4.8 ---->
`k=y*x` ---->
`k=4.8*5=24`

For x=5.5, y=4 ---->
`k=y*x` ---->
`k=5.5*4=22`

The values of k are different

therefore

The table A not represent an inverse variation

Verify table B

For x=0.1, y=300 ---->
`k=y*x` ---->
`k=300*0.1=30`

For x=0.5, y=60 ---->
`k=y*x` ---->
`k=60*0.5=30`

For x=75, y=0.4 ---->
`k=y*x` ---->
`k=75*0.4=30`

For x=100, y=0.3 ---->
`k=y*x` ---->
`k=100*0.30=30`

All the values of k are the same

therefore

The table B represent an inverse variation

The equation is equal to

`y*x=30`