Question

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

$x$	$6$	$8$	$10$	$\dots$	$20$
$y$	$15$	$20$	$\dots$	$40$	$\dots$

Answer 1

Complete the table

given:$x$ varies directly as $y$

$x$	$6$	$8$	$10$		$20$
$y$	$15$	$20$		$40$

As, $x$ and $y$ are in direct variation. Therefore, the ratio of the corresponding values of $x$ and $y$ remain constant.
Consider ‘k’ to be the constant of variation

When $x=6$ and $y=15$

$\Rightarrow k=\frac{x}{y}=\frac{6}{15}=\frac{2}{5}$

When $x=10$

$\frac{x}{y}=k\Rightarrow \frac{10}{y}=\frac{2}{5}\Rightarrow y=25$

When $y=40$

$\because \frac{x}{y}=k\Rightarrow \frac{x}{40}=\frac{2}{5}\Rightarrow x=16$

When $x=20$

$\frac{x}{y}=k\Rightarrow \frac{20}{y}=\frac{2}{5}\Rightarrow y=50$

Hence, the complete table is:

$x$	$6$	$8$	$10$	$16$	$20$
$y$	$15$	$20$	$25$	$40$	$50$