Question

Given that y varies inversely with x, if x =7 and y = 4, what is y when x = 2?

Answer 1

`y=14`

Explanation:

`y \propto 1/x`

`y=k/x`

`4=k/7`

`4 * 7 = k`

`28=k`

`y=28/x`

`y=28/(2)`

`y=14`

Answer 2

y = 14

Explanation:

y ∝
`(1)/(x)`

=> y =
`(k)/(x)` -------------(1)

Where k is the constant of proportionality

Now,

x = 7, y = 4

Putting in (1)

4 =
`(k)/(7)`

So,

=> k = 28

Now y = ? when x = 2

Putting x and k in (i)

y =
`(28)/(2)`

y = 14