[tex]\displaystyle\bf\\y=\frac{k}{x} \\\\\Big(1 \ ; \ 1\Big) \ \ \ \Rightarrow \ \ \ x=1 \ \ ; \ \ y=1\\\\\\1=\frac{k}{1} \\\\\boxed{k=1}[/tex]
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[tex]\displaystyle\bf\\y=\frac{k}{x} \\\\\Big(1 \ ; \ 1\Big) \ \ \ \Rightarrow \ \ \ x=1 \ \ ; \ \ y=1\\\\\\1=\frac{k}{1} \\\\\boxed{k=1}[/tex]