Question 7 Graph: y ≥ -X -5 -4 -3 -2 -1 Clear All Draw: 1 5+ Submit Question + 3 2 1 1 -2 -3 -4 -5+ > 2 3 4 -LA Question Help: Video Message instructor

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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### Question 7

**Graph: \( y \geq \frac{1}{4}x - 1 \)**

#### Description:

The graph displays a coordinate plane ranging from -5 to 5 on both the x-axis and y-axis. The grid is clearly marked with integers labeled at each axis tick.

#### Visual Elements:

- **Coordinate Plane**: 
  - The x-axis and y-axis intersect at the origin (0,0).
  - The plane shows equal spacing with grid lines to aid in accurate graphing.

- **Equation**: 
  - The inequality \( y \geq \frac{1}{4}x - 1 \) represents a line with a slope of \(\frac{1}{4}\) and a y-intercept at -1.
  - The graph of the inequality includes the region above and including the line.

- **Functional Tools Available**:
  - **Clear All**: A button to reset your drawing on the graph.
  - **Draw Options**: 
    - There are two icons allowing users to shade the area above or below the line according to the inequality. 
  - **Question Help**: 
    - **Video**: A link to a video for additional instructional support.
    - **Message Instructor**: An option to contact the instructor for help.
  - **Submit Question**: A button to submit your graph for evaluation.

Use these tools to accurately graph the inequality on the coordinate plane. Make sure to shade the correct region to represent \( y \geq \frac{1}{4}x - 1 \).
Transcribed Image Text:### Question 7 **Graph: \( y \geq \frac{1}{4}x - 1 \)** #### Description: The graph displays a coordinate plane ranging from -5 to 5 on both the x-axis and y-axis. The grid is clearly marked with integers labeled at each axis tick. #### Visual Elements: - **Coordinate Plane**: - The x-axis and y-axis intersect at the origin (0,0). - The plane shows equal spacing with grid lines to aid in accurate graphing. - **Equation**: - The inequality \( y \geq \frac{1}{4}x - 1 \) represents a line with a slope of \(\frac{1}{4}\) and a y-intercept at -1. - The graph of the inequality includes the region above and including the line. - **Functional Tools Available**: - **Clear All**: A button to reset your drawing on the graph. - **Draw Options**: - There are two icons allowing users to shade the area above or below the line according to the inequality. - **Question Help**: - **Video**: A link to a video for additional instructional support. - **Message Instructor**: An option to contact the instructor for help. - **Submit Question**: A button to submit your graph for evaluation. Use these tools to accurately graph the inequality on the coordinate plane. Make sure to shade the correct region to represent \( y \geq \frac{1}{4}x - 1 \).
Expert Solution
Step 1

A linear inequality is an inequality which involves a linear function. Linear inequalities are the expressions where any two values are compared by the inequality symbols. 

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