Question

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

x	3	5	8	11	26
y	9	15	24	33	78

(ii)

x	2.5	4	7.5	10	14
y	10	16	30	40	42

(iii)

x	5	7	9	15	18	25
y	15	21	27	60	72	75

Answer 1

(i)
$$\begin{gathered} \mathrm{Clearly},\frac{x}{y}=\frac{3}{9}=\frac{5}{15}=\frac{8}{24}=\frac{11}{33}=\frac{26}{78}=\frac{1}{3}\left(\mathrm{constant}\right) \\ \mathrm{Therefore},\mathrm{x}\mathrm{and}\mathrm{y}\mathrm{are}\mathrm{proportional}. \end{gathered}$$

(ii)
$$\begin{gathered} \mathrm{Clearly},\frac{x}{y}=\frac{2.5}{10}=\frac{4}{16}=\frac{7.5}{30}=\frac{10}{40}=\frac{1}{4},\mathrm{while}\frac{14}{42}=\frac{1}{3} \\ \mathrm{i}.\mathrm{e}.,\frac{2.5}{10}=\frac{4}{16}=\frac{7.5}{30}=\frac{10}{40}\mathrm{is}\mathrm{not}\mathrm{equal}\mathrm{to}\frac{14}{42}. \\ \mathrm{Therefore},x\mathrm{and}y\mathrm{are}\mathrm{not}\mathrm{proportional}. \end{gathered}$$

(iii)
$$\begin{gathered} \mathrm{Clearly},\frac{x}{y}=\frac{5}{15}=\frac{7}{21}=\frac{9}{27}=\frac{25}{75}=\frac{1}{3},\mathrm{while}\frac{15}{60}=\frac{18}{72}=\frac{1}{4} \\ \mathrm{i}.\mathrm{e}.,\frac{5}{15}=\frac{7}{21}=\frac{9}{27}=\frac{25}{75}\mathrm{is}\mathrm{not}\mathrm{equal}\mathrm{to}\frac{15}{60}\mathrm{and}\frac{18}{72}. \\ \mathrm{Therefore},x\mathrm{and}y\mathrm{are}\mathrm{not}\mathrm{proportional}. \end{gathered}$$