A varies directly to \(B\), then \(A\) is said to be in direct proportion to \(B\). It is written as

\(A\;\alpha \;B\) or \(A = kB\)

It can be understood with the typical example of percentage relating to expenses, consumption and price of the article. If \(A\) is directly proportional to \(B\), it simply means that the ratio \(\frac{A}{B}\) is constant. If \(A\) becomes double, \(B\) also become double; if \(A\) is reduced to one third, then b is also reduced to one third etc. Now suppose A is proportional to \({B^3},\) it means

\(A = k{B^3}\)or the ratio of \(A\) and \({B^3}\)is constant.

Now take a different case, suppose \(z\) is directly proportional to \(x\), when \(y\) is constant and directly proportional to \({y^2},\) when \(x\) is constant, then

\(z\; \propto x\) when \(y\) is constant and

\(z\; \propto {y^2},\) when \(x\) is  constant

Combining both the relations, we get,

\(z\; \propto x{y^2}\)