Question

Find the variation constant and an equation of variation where y varies inversely as x and y = 2 when x = 2.The variation constant is [__]The equation of variation is y =[___]

Answer 1

Variation constant is k = 4

Equation of variation,

y = (4/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 = 2 when x = 2

y = (k/x)

2 = (k/2)

Multiply both sides by 2

4 = k

So,

k = 4

Equation of variation,

y = (k/x)

k = 4

y = (4/x)