Question

Complete the following tables given that $x$ varies directly as $y$.

$\left(i\right)$

$x$	$2.5$	$\dots$	$\dots$	15
$y$	$5$	$8$	$12$	$\dots$

Answer 1

Complete the table

Given: $x$ varies directly as $y$

$x$	$2.5$	$\dots$	$\dots$	15
$y$	$5$	$8$	$12$	$\dots$

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 $x=2.5$ and $y=5$

$k=\frac{x}{y}=\frac{2.5}{5}=\frac{25}{50}=\frac{1}{2}$

$\Rightarrow k=\frac{1}{2}$

When $y=8$

$\because \frac{x}{y}=k\Rightarrow \frac{x}{8}=\frac{1}{2}\Rightarrow x=\frac{8}{2}\Rightarrow x=4$

When $y=12$

$\because \frac{x}{y}=k\Rightarrow \frac{x}{12}=\frac{1}{2}\Rightarrow x=6$

When $x=15$

$\because \frac{x}{y}=k\Rightarrow \frac{15}{y}=\frac{1}{2}\Rightarrow y=30$

Hence, the complete table is:

$x$	$2.5$	$4$	$6$	$15$
$y$	$5$	$8$	$12$	$30$