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Chapter 4: Q. 675 (page 574)

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

Write the inequality shown by the graph with the boundary line

x-2y=6.

Short Answer

Expert verified

The inequality shown by the graph isx-2y≤6.

Step by step solution

01

Step 1. Given Information

A graph with boundary line is 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 to the linear inequality if the pair of values satisfy the inequality when substituted.

03

Step 3. Determining the inequality

The boundary line x-2y=6has one side of the points satisfying x-2y>6and other side satisfying x-2y<6.

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

Let us consider .

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

x-2y>6⇒0>6 False.

x-2y<6⇒0<6 True.

And Origin is not in the shaded area of the graph.

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

Therefore the inequality graph represents is x-2y≤6.

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