Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 3 - Section 3.6 - Graphing Linear Inequalities in Two Variables - Exercise Set: 25


Refer to the image below for the graph.

Work Step by Step

To graph the given inequality, perform the following steps: (1) Graph the boundary line $x-y=6$ using a solid line since it involves $\le$. (refer to the image below for the graph) (2) Use the test point $(0, 0)$. Substitute the x and y values of this point into the given inequality to obtain: \begin{array}{ccc} \\&x-y&\le &6 \\&0-0 &\le &6 \\&0 &\le &6 \end{array} The statement is true. (3) The resulting statement in step (2) is true. This means that the solution set is the region that contains the test point $(0, 0)$. To complete the graph, shade the region that contains $(0, 0)$. (refer to the attached image in the answer part above for the graph)
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