Precalculus (6th Edition) Blitzer

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

Chapter 7 - Cumulative Review Exercises - Page 880: 23


The graph is shown below:

Work Step by Step

Substitute the equal symbol in place of the inequality symbol and graph the linear equation. By finding any two solutions of the linear equation, plot the graph of the linear equation $2x-3y=6$ To find the value of the x-intercept, substitute $ y=0$ as given below: $\begin{align} & 2x-3\left( 0 \right)=6 \\ & 2x=6 \\ & x=\frac{6}{2} \\ & x=3 \end{align}$ To find the value of the y-intercept, substitute $ x=0$ as given below: $\begin{align} & 2\left( 0 \right)-3y=6 \\ & -3y=6 \\ & y=-\frac{6}{3} \\ & y=-2 \end{align}$ Plot the intercepts $\left( 3,0 \right)\text{ and }\left( 0,-2 \right)$ and draw a solid line passing through these points because the inequality contains the $\le $ symbol in which the equality is included. Then, this solid line divides the plane in 3 parts: the line itself and the two half planes Now, choose a test point in any half plane; the test point is $\left( 0,0 \right)$. And check if the test point satisfies the inequality: $\begin{align} 2x-3y\le 6 & \\ 2\left( 0 \right)-3\left( 0 \right)\overset{?}{\mathop{\le }}\,6 & \\ 0\le 6 & \\ \end{align}$ Which is correct. Since the test point satisfies the inequality, shade the half plane containing that test point (that is, the origin).
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