Question

Complete the following tables given that $x$ varies directly as $y$.
$\left(iv\right)$

$x$	$4$	$9$	$\dots$	$\dots$	$3$	$\dots$
$y$	$16$	$\dots$	$48$	$36$	$\dots$	$4$

Answer 1

Complete the table

Given:$x$ varies directly as $y$.

$x$	$4$	$9$	$\dots$	$\dots$	$3$	$\dots$
$y$	$16$	$\dots$	$48$	$36$	$\dots$	$4$

As, $x$ and $y$ are in direct variation. Therefore, the ratio of the corresponding values of $x$ and $y$ remain constant.
Consider ${}^{\prime }{k}^{\prime }$ to be the constant of variation

When $x=4$ and $y=16$

$\Rightarrow k=\frac{x}{y}=\frac{4}{16}=\frac{1}{4}$

When $x=9$

$\frac{x}{y}=k\Rightarrow \frac{9}{y}=\frac{1}{4}\Rightarrow y=36$

When $y=48$

$\because \frac{x}{y}=k\Rightarrow \frac{x}{48}=\frac{1}{4}\Rightarrow x=12$

When $y=36$

$\because \frac{x}{y}=k\Rightarrow \frac{x}{36}=\frac{1}{4}\Rightarrow x=9$

When $x=3$

$\frac{x}{y}=k\Rightarrow \frac{3}{y}=\frac{1}{4}\Rightarrow y=12$

When $x=4$

$\because \frac{x}{y}=k\Rightarrow \frac{x}{4}=\frac{1}{4}\Rightarrow x=1$

Hence, the complete table is:

$x$	$4$	$9$	$12$	$9$	$3$	$1$
$y$	$16$	$36$	$48$	$36$	$12$	$4$