Chapter 4: Q. 4.139 (page 548)

Write the inequality shown by the graph with the boundary line $y = - 2 x + 3$

Short Answer

Expert verified

The inequality shown by the graph is $y \geq - 2 x + 3$ .

Step by step solution

Step 1. Given Information

We are given an equation $y = - 2 x + 3$ and a graph,

Step 2. Finding the inequality

The line $y = - 2 x + 3$ is the boundary line. On one side of the line are the points with $y > - 2 x + 3$ and on the other side of the line are the points with $y < - 2 x + 3$ .

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

$y > - 2 x + 3 0 > - 2 (0) + 3 0 > 3$

False.

$y < - 2 x + 3 0 < - 2 (0) + 3 0 < 3$

True,

Since $y > - 2 x + 3$ is false for $(0, 0)$ which is not the part of shaded region, hence tshaded region is the solution for the inequality $y > - 2 x + 3$

Also, the boundary line is graphed with a solid line.

Hence the inequality includes the equal sign.

$y \geq - 2 x + 3$

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Write the inequality shown by the graph with the boundary line $y = - 2 x + 3$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the inequality

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Write the inequality shown by the graph with the boundary line y=−2x+3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the inequality

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Decision Maths

Statistics

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Write the inequality shown by the graph with the boundary line $y = - 2 x + 3$