Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 7 - Test - Page 879: 7


The graph is shown below:

Work Step by Step

Let us consider the inequalities $ x-2y<8$; substitute the equals symbol in place of the inequality and rewrite the equation as given below: By finding any two solutions of the linear equation, plot the graph of the linear equation $ x-2y=8$: To find the value of the x-intercept, substitute y = 0 as follows: $\begin{align} & x-2\left( 0 \right)=8 \\ & x=8 \\ \end{align}$ To find the value of the y-intercept, substitute x = 0 as follows: $\begin{align} & 0-2y=8 \\ & y=-4 \\ \end{align}$ Plot the intercepts $\left( 8,0 \right)\text{ and }\left( 0,-4 \right)$ and draw a dotted line passing through these points because the inequality does not contain the equal symbol. Now this dashed line divides the plane in 3 region: the line itself, and the two half planes. Now, take the origin $\left( 0,0 \right)$ as a test point and check the region in the graph to shade: Check if the test point satisfies the inequality. $ x-2y<8$ $0-2*0<8$ $0<8$ This is true, so the origin is included. See the final graph below.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.