Question

Complite the following table given that x varies directly as y . 

x	4	9	...	...	3	...
y	16	...	48	36	...	4

Answer 1

\[\text{ Here, x and y vary directly }  . \]
\[ \therefore x = ky\]

\[ x = 4 \text{ and }  y = 16\]
\[i . e . , 4 = k \times 16\]
\[ \Rightarrow k = \frac{4}{16} = \frac{1}{4}\]
\[\text{ For x = 9 and } k = \frac{1}{4}, \text{ we have: }  \]
\[9 = ky\]
\[ \Rightarrow y = 4 \times 9 = 36\]
\[\text{ For y = 48 and } k = \frac{1}{4}, \text{ we have: } \]
\[x = ky\]
\[ = \frac{1}{4} \times 48 = 12\]
\[\text{ For y = 36 and } k = \frac{1}{4}, \text{ we have: }  \]
\[x = ky\]
\[ = \frac{1}{4} \times 36 = 9\]
\[\text{ For x = 3 and } k = \frac{1}{4}, \text{ we have } : \]
\[x = ky\]
\[ \Rightarrow 3 = \frac{1}{4} \times y\]
\[ \Rightarrow y = 12\]
\[\text{ For y = 4 and } k = \frac{1}{4}, \text{ we have} : \]
\[x = ky\]
\[ = \frac{1}{4} \times 4 = 1\]