Chapter 4: Q. 4.142 (page 550)

Write the inequality shown by the shaded region in the graph with the boundary line $3 x - y = 6$

Short Answer

Expert verified

The inequality shown by the graph is $3 x - y \geq 6$ .

Step by step solution

Step 1. Given Information

We are given an equation $3 x - y = 6$ and a graph,

Step 2. Finding the inequality

The line $3 x - y = 6$ is the boundary line. On one side of the line are the points with $3 x - y > 6$ and on the other side of the line are the points with $3 x - y < 6$ .

Checking the inequality with point $(0, 0)$ ,

role="math" $3 x - y > 6 3 (0) - 0 > 6 0 > 6$

False.

Step 3. Finding the inequality

Checking the inequality with point $(0, 0)$ ,

$3 x - y < 6 3 (0) - 0 < 6 0 < 6$

True.

Since $3 x - y > 6$ is false for $(0, 0)$ which is not the part of shaded region, hence shaded region is the solution for the inequality role="math" localid="1647585928644" $3 x - y > 6$

Also, the boundary line is graphed with a solid line, the inequality includes the equal sign.

$3 x - y \geq 6$

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Write the inequality shown by the shaded region in the graph with the boundary line $3 x - y = 6$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the inequality

Step 3. Finding the inequality

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Write the inequality shown by the shaded region in the graph with the boundary line 3x−y=6

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the inequality

Step 3. Finding the inequality

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

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Study anywhere. Anytime. Across all devices.

Write the inequality shown by the shaded region in the graph with the boundary line $3 x - y = 6$