Question

Complete the following table in which $x\propto y$:

$x$	$y$
$4$	$12$
$5$	$15$
$2$	....
....	$21$
$3$	....

Answer 1

It is given that,
$x\propto y$
$x=ky$
Constant of variation, $k=\frac{x}{y}=\frac{4}{12}=\frac{1}{3}$
Given table:
Third case: $x=2,k=\frac{1}{3}$
$\Rightarrow y=\frac{x}{k}$
$\Rightarrow y=3\times 2=6$

$\Rightarrow y=6$ ....(i)
Fourth case: $y=21$
$\Rightarrow x=ky$
$\Rightarrow x=\frac{21}{3}=7$

$\Rightarrow x=7$ ....(ii)
Fifth case: $x=3$
$\Rightarrow y=\frac{x}{k}$
$\Rightarrow y=3\times 3=9$

$\Rightarrow y=9$ ....(iii)

(i), (ii) and (iii) is the desired result.