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

$x$ $3$ $5$ $7$ $9$

$y$ $\dots$ $20$ $28$ $\dots$

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Solution

Complete the table

Given: $x$ varies directly as $y$

$x$ $3$ $5$ $7$ $9$

$y$ $20$ $28$

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 $x = 5$ and $y = 20$
$\Rightarrow k = \frac{x}{y} = \frac{5}{20} = \frac{1}{4}$

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

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

Hence, the complete table is:

$x$ $3$ $5$ $7$ $9$

$y$ $12$ $20$ $28$ $36$

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