# Chapter 11 - Rational Expressions and Functions - 11-6 Inverse Variation - Practice and Problem-Solving Exercises - Page 691: 36

$x = \frac{1}{6}$

#### Work Step by Step

Our equation for an inverse variation is $y = \frac{k}{x}$ or $xy = k$ or, as will be needed in this problem, $x = \frac{k}{y}$. We will use the second form of the equation to solve for k. We use the ordered pair (\frac{1}{3},\frac{1}{4}) to solve for k, from which we know that $x = \frac{1}{3}$ and $y = \frac{1}{4}$. $\frac{1}{3}\times\frac{1}{4}= k$ $\frac{1}{12} = k$ So, $k = \frac{1}{12}$ Therefore, our equation for the inverse variation is $y = \frac{\frac{1}{12}}{x}$ or $xy = \frac{1}{12}$ or $x = \frac{\frac{1}{12}}{y}$ Using the third form of the equation, $x = \frac{\frac{1}{12}}{y}$, we can use the y value of the second order pair to find our missing x value. $x = \frac{\frac{1}{12}}{\frac{1}{2}}$ $x = \frac{1}{6}$

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