Below is a graph a system A y>-x-4 y≤ x +3 By2-x-4 yx+3 9 B N 61 -24 -3 -5. 6- What is the system of inequalities in slope-intercept form? -7 -Bi 1 2 4 6 8 9
Below is a graph a system A y>-x-4 y≤ x +3 By2-x-4 yx+3 9 B N 61 -24 -3 -5. 6- What is the system of inequalities in slope-intercept form? -7 -Bi 1 2 4 6 8 9
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Below is a graph of a system of inequalities.
![**Graphing Systems of Inequalities: Understanding Linear Inequalities**
*Below is a graph of a system of inequalities.*
![Graph of a system of inequalities]
The graph displays two linear inequalities represented by different boundary lines and shading which depict the solution region. Let's break down what’s presented in the graph.
### Explanation of the Graph
- **Red Line (Solid):** This line appears to represent an inequality with the boundary equation and is shaded above it. It implies the inequality is either non-strict (greater or less than or equal to).
- **Blue Line (Dashed):** This line has a boundary equation and is shaded below it, likely representing a strict inequality (greater than or less than).
**What is the system of inequalities in slope-intercept form?**
### Multiple Choice Options:
A)
\[ y > -\frac{3}{2}x - 4 \]
\[ y \leq x + 3 \]
B)
\[ y \geq -\frac{2}{3}x - 4 \]
\[ y < x + 3 \]
C)
\[ y \leq -\frac{2}{3}x - 4 \]
\[ y > x + 3 \]
Students should analyze the graph to determine which inequalities correctly describe the shaded regions separated by the boundary lines. Pay attention to the slope, y-intercept, and whether each line is dashed or solid, as well as where the shading occurs in relation to each line.
**Interactive Question:**
- Review the slopes and intercepts carefully.
- Identify whether the boundaries are inclusive (solid line) or exclusive (dashed line).
- Relate the shaded areas to the inequality signs (greater or less than, and/or equal to).
**Select the correct system of inequalities.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2e590b60-6a59-44a7-87c2-f928710b5b97%2F14564177-2ac3-4229-a243-79802b2d151f%2Fskol937_processed.png&w=3840&q=75)
Transcribed Image Text:**Graphing Systems of Inequalities: Understanding Linear Inequalities**
*Below is a graph of a system of inequalities.*
![Graph of a system of inequalities]
The graph displays two linear inequalities represented by different boundary lines and shading which depict the solution region. Let's break down what’s presented in the graph.
### Explanation of the Graph
- **Red Line (Solid):** This line appears to represent an inequality with the boundary equation and is shaded above it. It implies the inequality is either non-strict (greater or less than or equal to).
- **Blue Line (Dashed):** This line has a boundary equation and is shaded below it, likely representing a strict inequality (greater than or less than).
**What is the system of inequalities in slope-intercept form?**
### Multiple Choice Options:
A)
\[ y > -\frac{3}{2}x - 4 \]
\[ y \leq x + 3 \]
B)
\[ y \geq -\frac{2}{3}x - 4 \]
\[ y < x + 3 \]
C)
\[ y \leq -\frac{2}{3}x - 4 \]
\[ y > x + 3 \]
Students should analyze the graph to determine which inequalities correctly describe the shaded regions separated by the boundary lines. Pay attention to the slope, y-intercept, and whether each line is dashed or solid, as well as where the shading occurs in relation to each line.
**Interactive Question:**
- Review the slopes and intercepts carefully.
- Identify whether the boundaries are inclusive (solid line) or exclusive (dashed line).
- Relate the shaded areas to the inequality signs (greater or less than, and/or equal to).
**Select the correct system of inequalities.**
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