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: 25


Direct Variation $y = \frac{x}{2}$

Work Step by Step

A quick way to recognize direct and inverse variation is to ask, "as x goes up in value, what does y do?" If y goes up, then it is a direct variation. If y goes down, then it is an inverse variation. In this case, as x goes up, y also goes up, meaning it is a direct variation. Another way is to check each ratio of \frac{y}{x}. If the result is the same answer for each, then it is a direct variation and we have found our k value. $\frac{1}{2} =\frac{1}{2} $ $\frac{2.5}{5} = \frac{1}{2} $ $\frac{4}{8} = \frac{1}{2} $ Again, we see that it is a direct variation and $k=\frac{1}{2}$ Therefore, the equation for this direct variation is: $y=\frac{1}{2}x$ or $y=\frac{x}{2}$
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