Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 6 - Systems of Equations and Inequalities - 6-5 Linear Inequalities - Practice and Problem-Solving Exercises - Page 398: 33


$y \gt \frac{3}{2}x -3$

Work Step by Step

The slope of the line is $\frac{3}{2}$ and the y-intercept is $-3$, so the equation of the boundary line is $y = \frac{3}{2}x -3$. The boundary line is dashed, so the inequality symbol is either $\lt$ or $\gt$. Assume $y \lt \frac{3}{2}x -3$ and test a point in the region to see whether it satisfies this equation. For example, test the point $(1, -1)$. $-1 \lt \frac{3}{2}(-1) -3$ $-1 \lt \frac{-9}{2}$ This is not true. Therefore, the correct inequality is $y \gt \frac{3}{2}x -3$.
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