Question

If z varies directly with the product of x and y(z=k x y) , then z is said to vary jointly with x and y .

Answer 1

The value of z varies jointly with w and y.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of constant of variation

let k be the constant of proportion

When a quantity varies directly with others, then we have a relation, y = kx

Given relation is z = kxy        —-- 1

Also x varies directly with w i.e. x = k'w, where k' is constant of variation for x and w

Using in equation 1, we have,

z = k(k'w)y

z = kk'wy

z = Kwy, where K is constant of variation i.e. K = kk'

It shows that z varies directly with w and y.

Hence, z varies jointly with w and y.

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