Question

Observe the tables given below and in each case find whether x and y are inversely proportional :

(i) $\begin{array}{ccccc}x& 6& 10& 14& 16\\ y& 9& 15& 21& 24\end{array}$

(ii) $\begin{array}{cccccc}x& 5& 9& 15& 3& 45\\ y& 18& 10& 6& 30& 2\end{array}$

(iii) $\begin{array}{ccccc}x& 9& 3& 6& 36\\ y& 4& 12& 9& 1\end{array}$

Answer 1

$\because$ x and y are inversely proportional

Then xy are equal

(i) $xy=6\times 9=54=10\times 15=150=14\times 21=294=16\times 24=384$

$\because$ xy in each is not equal

So, x and y are not inversely proportional

(ii) $xy=5\times 18=90=9\times 10=90=15\times 6=90=3\times 30=90=45\times 2=90$

$\because$ xy in each case is equal

$\therefore$ x and y are inversely proportional

(iii) $xy=9\times 4=36=3\times 12=36=6\times 9=54=36\times 1=36$

$\because$ xy in each is not equal

$\therefore$ x and y are not inversely propotional