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: 32


$y \geq -3x +3$

Work Step by Step

The slope of the line is $-3$ and the y-intercept is $3$, so the equation of the boundary line is $y = -3x +3$. The boundary line is solid, so the inequality symbol is either $\leq$ or $\geq$. Assume $y \leq -3x +3$ and test a point in the region to see whether it satisfies this equation. For example, test the point $(2, 3)$. $3 \leq -3(2) +3$ $3 \leq -6$ This is not true. Therefore, the correct inequality is $y \geq -3x +3$
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