Question

If x and y vary directly and x = 3 when y = 9, then find constant of variation. ​

Answer 1

K=1/3

Pls check the below image for explanation

Answer 2

The constant of proportionality/variation is 1/3.

Given:

x and y vary directly and  x = 3 when y = 9.

To Find:

The constant of variation.

Solution:

If two numbers 'a' and 'b' vary directly, it means that as the value of 'x' increases/decreases, the value of 'y' also increases/decreases and vice versa. It is represented by the symbol '∝'.

Hence, a∝b.

The above equation can be written in terms of equality by introducing a constant 'k' on either side of the above expression.

So, a=kb, where 'k' is the constant of proportionality/variation.

We are given that x and y vary directly, i.e. x∝y.

Also, x = 3 when y = 9.

Now, x = 3 = (1/3)9 = (1/3)y

Let us assume that k = 1/3.

Hence, x∝y ⇒ x = k3.

∴ The constant of proportionality/variation is 1/3.

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