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# If $y \propto \dfrac{1}{x}$ and $x = 7$ when $y = 9$, find the constant of variation $\left( k \right)$.

Last updated date: 27th Mar 2023
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Given $y \propto \dfrac{1}{x}$
Let the constant of variation introduced be $k$ after removing the proportionality sign.
$y \propto \dfrac{1}{x} \Rightarrow y = k\left( {\dfrac{1}{x}} \right){\text{ }} \to {\text{(1)}}$
Also given that when $y = 9$, the corresponding value of $y$ is $y = 9$.
Put $x = 7$ and $y = 9$ in equation (1), we get
$\Rightarrow y = k\left( {\dfrac{1}{x}} \right){\text{ }} \Rightarrow 9 = k\left( {\dfrac{1}{7}} \right) \Rightarrow k = 7 \times 9 = 63$
Therefore, the required value of the constant of variation $\left( k \right)$ is 63.