https://file.aiquickdraw.com/mathbot/file/1726110399342v5vmn95c.jpg

To match each graph to the corresponding inequality, let's analyze each one:

1. **Top Graph**:
   - **Key Features**: The shaded region is below a dashed line with a negative slope.
   - **Conclusion**: The inequality represented here is \( y < mx + c \) because the region below the line is shaded, and the line is dashed, indicating a strict inequality (without the equal sign). 

2. **Middle Graph**:
   - **Key Features**: The shaded region is above a dashed line with a negative slope.
   - **Conclusion**: The inequality here is \( y > mx + c \) because the region above the line is shaded, and the dashed line indicates a strict inequality.

3. **Bottom Graph**:
   - **Key Features**: The shaded region is above a solid line with a positive slope.
   - **Conclusion**: The inequality here is \( y \geq mx + c \) because the region above the line is shaded, and the line is solid, indicating a non-strict inequality (with the equal sign).

Thus, the inequalities for the graphs from top to bottom are:

1. \( y < mx + c \)
2. \( y > mx + c \)
3. \( y \geq mx + c \)

Do you want more details on this, or have any questions?

Here are some related questions you might find useful:
1. How does the slope of the line affect the inequality?
2. What does it mean when the line is dashed versus solid?
3. How would the inequality change if the shaded region were on the other side of the line?
4. Can these inequalities represent real-world situations?
5. How does changing the y-intercept affect the inequality?

**Tip**: Always check whether the line in the graph is solid or dashed to determine whether the inequality is strict (`<`, `>`) or non-strict (`≤`, `≥`).

Match each graph to the inequality that it represents.

Analyze and solve graph inequality problems by identifying shaded regions and understanding the significance of solid and dashed boundary lines. Learn key concepts such as linear inequalities, shading rules, and slope properties for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation