Question

If y varies directly as x, and y is 6 when x is 72, which is the value of y when x is 8 ?

Answer 1

y =
`(2)/(3)`

given y ∝ x

To convert to an equation multiply by k the constant of variation

y = kx

to find k use the given condition y = 6 when x = 72

y = kx ⇒ k =
`(y)/(x)` =
`(6)/(72)` =
`(1)/(12)`

equation is → y =
`(1)/(12)` x

when x = 8 then

y =
`(1)/(12)` × 8 =
`(8)/(12)` =
`(2)/(3)`

Answer 2

`(y)/(x) = k`

`(6)/(72) = k`

`(1)/(12) = k`

********************************

`(y)/(x) = k`

`(y)/(8) = (1)/(12)`

12y = 8

`y = (8)/(12)`

`y = (2)/(3)`