Chapter 7 - Functions and Graphs - 7.5 Formulas, Applications, and Variation - 7.5 Exercise Set - Page 487: 53

variation constant $=k=9$ equation of the variation: $y=\frac{9}{x}$

Work Step by Step

$y$ varies inversely as $x$ so the variation is inverse. The equation of an inverse variation is of the form $y=\frac{k}{x}$ where $k$ is the constant of variation. To find the value of $k$ substitute the given values of $x$ and $y$ into $y=\frac{k}{x}$ to obtain: $$y=\frac{k}{x} \\27=\dfrac{k}{\frac{1}{3}} \\27 = k \cdot \frac{3}{1} \\27=3k \\\frac{27}{3}=\frac{3k}{3} \\9=k$$ Thus, the equation of the variation is $y=\frac{9}{x}$.

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