Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 7 - Algebra: Graphs, Functions, and Linear Systems - Chapter Summary, Review, and Test - Review Exercises - Page 482: 50

Answer

See below:

Work Step by Step

Step 1: Convert the inequality to an equation by replacing \[\ge \] by = sign. \[2x+3y=12\] Step 2: Graph the equation using intercept form or slope-intercept form. Make \[x=0\] to find the y-intercept, \[\begin{align} & 2x+3y=12 \\ & 0+3y=12 \\ & y=4 \end{align}\] Make \[y=0\] to find x-intercept, \[\begin{align} & 2x+3y=12 \\ & 2x+0=12 \\ & x=6 \end{align}\] So, the line passes through \[\left( 6,0 \right)\]and \[\left( 0,4 \right)\]. The line is solid since the inequality contains the \[\ge \]symbol. Step 3: Choose a test point. The origin \[\left( 0,0 \right)\]be the test point. Substituting in the inequality \[\begin{align} & 2x+3y\ge 12 \\ & 0\ge 12 \end{align}\] The statement is false. The graph does not contain the test point.
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