Chapter 4: Q. 673 (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
$y = \frac{2}{3} x - 3$

Short Answer

Expert verified

The inequality shown by the graph is $y ⩾ \frac{2}{3} x - 3$

Step by step solution

Step 1. Given Information

A graph with boundary line $y = \frac{2}{3} x - 3$ is given.

We have to find the inequality the graph represents.

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.

Step 3. Determining the inequality

The boundary line $y = \frac{2}{3} x - 3$ has one side of the points satisfying $y < \frac{2}{3} x - 3$ and other side satisfying $y > \frac{2}{3} x - 3$ .

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

Let us consider .

Check which inequality the point satisfies.

$y < \frac{2}{3} x - 3 \Rightarrow 0 < 0 - 3 \Rightarrow 0 < - 3$ False.

$y > \frac{2}{3} x - 3 \Rightarrow 0 > 0 - 3 \Rightarrow 0 > - 3$ True.

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

Therefore the inequality graph represents is $y ⩾ \frac{2}{3} x - 3$ .

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In the following exercises, write the inequality shown by the shaded region.
Write the inequality shown by the graph with the boundary line
$y = \frac{2}{3} x - 3$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Definition of a solution

Step 3. Determining the inequality

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In the following exercises, write the inequality shown by the shaded region.Write the inequality shown by the graph with the boundary liney=23x-3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Definition of a solution

Step 3. Determining the inequality

One App. One Place for Learning.

Most popular questions from this chapter

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Theoretical and Mathematical Physics

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In the following exercises, write the inequality shown by the shaded region.
Write the inequality shown by the graph with the boundary line
$y = \frac{2}{3} x - 3$