Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 11 - Rational Expressions and Functions - 11-6 Inverse Variation - Practice and Problem-Solving Exercises - Page 691: 35


$x = 5$

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 (2.5,4) to solve for k, from which we know that $x = 2.5$ and $y = 4$. $2.5\times4 = k$ $ 10 = k$ So, $k = 10$ Therefore, our equation for the inverse variation is $y = \frac{10}{x}$ or $xy = 10$ or $x = \frac{10}{y}$ Using the third form of the equation, $x = \frac{10}{y}$, we can use the y value of the second order pair to find our missing x value. $x = \frac{10}{2}$ $x = 5$
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