Question

If y varies inversely as x, find the constant of variation k and the inverse variation equation for the situationy=3 when x=9

Answer 1

The constant of variation is

k = 27

We can then write the inverse variation equation by substituting the value of k

y = (k/x)

y = (27/x)

Step-by-step explanation

We are told that y varies inversely as x, which can be written as

y ∝ (1/x)

Introducing the constant of variation, k, we have

y ∝ (1/x)

y = k(1/x)

y = (k/x)

We can then solve for k knowing that

y = 3 when x = 9

y = (k/x)

3 = (k/9)

We can rewrite this as

(k/9) = 3

Multiply both sides by 9

(k/9) × 9 = 3 × 9

k = 27

Hope this Helps!!!