Question

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

(i) $\begin{array}{cccccc}x& 3& 5& 8& 11& 26\\ y& 9& 15& 24& 33& 78\end{array}$

(ii) $\begin{array}{cccccc}x& 2.5& 4& 7.5& 10& 14\\ y& 10& 16& 30& 40& 42\end{array}$

(iii) $\begin{array}{ccccccc}x& 5& 7& 9& 15& 18& 25\\ y& 15& 21& 27& 60& 72& 75\end{array}$

Answer 1

(1) $\frac{x}{y}=\frac{3}{9}=\frac{1}{3}=\frac{5}{15}=\frac{1}{3}=\frac{8}{24}=\frac{1}{3}=\frac{11}{33}=\frac{1}{3}=\frac{26}{78}=\frac{1}{3}\text{In each case}\frac{x}{y}=\frac{1}{3}\therefore \text{x and y are proportional}$

(ii) $\frac{x}{y}=\frac{2.5}{10}=\frac{1}{4}=\frac{4}{16}=\frac{1}{4}=\frac{7.5}{30}=\frac{1}{4}=\frac{10}{40}=\frac{1}{4}=\frac{14}{42}=\frac{1}{3}not\frac{1}{4}\because \text{x and y are not proportional}$

(iii) $\frac{x}{y}=\frac{5}{15}=\frac{1}{3}=\frac{7}{21}=\frac{1}{3}=\frac{9}{27}=\frac{1}{3}=\frac{10}{40}=\frac{1}{4}\ne \frac{1}{3}=\frac{14}{42}=\frac{1}{3}\therefore \text{x and y are not proportional}$