Question

Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation. Y=4.5 when x=3

Answer 1

If y in inversely proportional to x


`y=k* (1)/(x)`


And for:
y=4.5 and x=3 :

`4.5=k* (1)/(3) \\~\\ k= (27)/(2) =13.5`

Answer 2

k = 13.5

xy = 13.5

Explanation:

Inverse variation states:

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

then, the equation is in the form of:

`y = (k)/(x)` where, k si the constant of variation.

or xy = k ......[1]

As per the statement:

Given: y = 4.5 and x = 3

Using the definition of inverse variation, solve for k;

Substitute the given values in [1] we have;

`4.5 \cdot 3 =k`

⇒13.5 = k

then, we get equation:

`xy = 13.5`

Therefore, the constant of variation(k) is, 13.5 and an equation for the inverse variation is, xy = 13.5