Question

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

$x$	$5$	$\dots$	$10$	$35$	$25$	$\dots$
$y$	$8$	$12$	$\dots$	$\dots$	$\dots$	$32$

Answer 1

Complete the table

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

$x$	$5$	$\dots$	$10$	$35$	$25$	$\dots$
$y$	$8$	$12$	$\dots$	$\dots$	$\dots$	$32$

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 $x=5$ and $y=8$

$\Rightarrow k=\frac{x}{y}=\frac{5}{8}$

When $y=12$

$\because \frac{x}{y}=k\Rightarrow \frac{x}{12}=\frac{5}{8}\Rightarrow x=\frac{60}{8}\Rightarrow x=7.5$

When $x=10$

$\because \frac{x}{y}=k\Rightarrow \frac{10}{y}=\frac{5}{8}\Rightarrow y=\frac{80}{5}\Rightarrow y=16$

When $x=35$

$\frac{x}{y}=k\Rightarrow \frac{35}{y}=\frac{5}{8}\Rightarrow y=56$

$x$	$5$	$\dots$	$10$	$35$	$25$	$\dots$
$y$	$8$	$12$	$\dots$	$\dots$	$\dots$	$32$

When $x=25$

$\frac{x}{y}=k\Rightarrow \frac{25}{y}=\frac{5}{8}\Rightarrow y=40$

When $y=32$

$\because \frac{x}{y}=k\Rightarrow \frac{x}{32}=\frac{5}{8}\Rightarrow x=20$

Hence, the complete table is:

$x$	$5$	$7.5$	$10$	$35$	$25$	$20$
$y$	$8$	$12$	$16$	$56$	$40$	$32$