Question

Suppose that y varies inversely with x. Use the information to find k, and then choose the equation of variation. x = 2.5 when y = 100.

Answer 1

2.5x40=100 100/40=2.5

Answer 2

constant of variation(k) is, 250.

`y = (250)/(x)`

Explanation:

The inverse variation says that:

`y \propto (1)/(x)`

then, the equation is in the form of :

`y = (k)/(x)` ....[1] where, k is the constant of variation

As per the statement:

Suppose that y varies inversely with x.

then,

by definition of inverse variation we have;

`y = (k)/(x)`

When x = 2.5 and y = 100 then

Substitute these in [1] we have;

`100 = (k)/(2.5)`

Multiply 2.5 both sides we have;

`250 = k`

or

k = 250

⇒
`y = (250)/(x)`

Therefore, the constant of variation is, 250 and the equation we get
`y = (250)/(x)`