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Chapter 4: Q. 672 (page 573)

In the following exercises, write the inequality shown by the shaded region.

Write the inequality shown by the graph with the boundary line

y=-x+2.

Short Answer

Expert verified

The inequality shown by the graph isy猢�-x+2.

Step by step solution

01

Step 1. Given Information

A graph with boundary liney=-x+2is given.

We have to find the inequality the graph represents.

02

Step 2. Definition of a solution

An ordered pair (x,y)is a solution of the linear inequality if the pair of values satisfy the inequality when substituted.

03

Step 3. Determining the inequality

The boundary line y=-x+2has one side of the points satisfying y>-x+2and other side satisfying y<-x+2.

Consider a point in the shaded area in the given graph.

Let us consider (0,0).

Check which inequality the point (0,0)satisfies.

y>-x+2鈬�0>-0+2鈬�0>2 False.

y<-x+2鈬�0<-0+2鈬�0<2 True.

Since the boundary line is marked with a solid line, equal to sign is also included.

Therefore the inequality graph represents isy猢�-x+2.

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