Algebra 1

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

Chapter 5 - Linear Functions - 5-2 Direct Variation - Practice and Problem-Solving Exercises: 41

Answer

The student is wrong because the test he is performed is incorrect.

Work Step by Step

The student makes an error because it does not matter how each x coordinate increases and how each y coordinate increases. What matters is the ration of $\frac{y}{x}$. If that ration is constant for each x-coordinate and its respective y-coordinate, then we can deduce that the function is a direct variation. In this scenario, lets use this test to see if the rations are constant: 3/0=undefined 4/1=4 5/2=2.5 Since, "undefined" $\ne$ 4 $\ne$ 2.5, we can deduce that this function is not a direct variation.
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