Algebra 1

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

Chapter 5 - Linear Functions - 5-2 Direct Variation - Lesson Check: 5

Answer

Always

Work Step by Step

The reason why any equation with a form of y=kx will always pass through the origin (0,0) because no matter what k is, when you plug in 0 for both x and y, you will get 0=0 which is always true. You can also look at graphically. There is no vertical transformation with the graph but only a horizontal or vertical compression depending on k so the only thing the line can change is by how steep it gets. The graph can never go up or down so it has to pass through the origin.
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