Which of the following graphs represents the region defined by the inequality y> 4x - y

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Educational Content: Graphing Linear Inequalities**

**Task:**
Analyze the graphs to determine which one represents the inequality \( y > 4x - 3 \).

**Description of Graphs:**

1. **Graph 1:**
   - **Line Description:** Solid, diagonal line angled upwards intercepting the y-axis at -3.
   - **Shaded Region:** The region to the right of the line is shaded.

2. **Graph 2:**
   - **Line Description:** Dashed, diagonal line intercepting the y-axis at -3.
   - **Shaded Region:** The region to the right of the line is shaded.

3. **Graph 3:**
   - **Line Description:** Solid, diagonal line intercepting the y-axis at -3.
   - **Shaded Region:** The region to the left of the line is shaded.

4. **Graph 4:**
   - **Line Description:** Dashed, diagonal line intercepting the y-axis at -3.
   - **Shaded Region:** The region to the left of the line is shaded.

**Solution:**
The inequality \( y > 4x - 3 \) is represented with a dashed line (since the inequality is strict, ">") with the region above (or to the right of) the line being shaded.

- **Correct Graph:** Graph 2 represents the inequality correctly with a dashed line and shading to the right.
Transcribed Image Text:**Educational Content: Graphing Linear Inequalities** **Task:** Analyze the graphs to determine which one represents the inequality \( y > 4x - 3 \). **Description of Graphs:** 1. **Graph 1:** - **Line Description:** Solid, diagonal line angled upwards intercepting the y-axis at -3. - **Shaded Region:** The region to the right of the line is shaded. 2. **Graph 2:** - **Line Description:** Dashed, diagonal line intercepting the y-axis at -3. - **Shaded Region:** The region to the right of the line is shaded. 3. **Graph 3:** - **Line Description:** Solid, diagonal line intercepting the y-axis at -3. - **Shaded Region:** The region to the left of the line is shaded. 4. **Graph 4:** - **Line Description:** Dashed, diagonal line intercepting the y-axis at -3. - **Shaded Region:** The region to the left of the line is shaded. **Solution:** The inequality \( y > 4x - 3 \) is represented with a dashed line (since the inequality is strict, ">") with the region above (or to the right of) the line being shaded. - **Correct Graph:** Graph 2 represents the inequality correctly with a dashed line and shading to the right.
**Question:**

2. The shaded region of the graph represents which inequality?

**Graph Explanation:**

The graph shows a coordinate plane with a dashed line. The line has a negative slope, crossing the y-axis at (0, 1) and the x-axis at (3.5, 0). The region below the dashed line is shaded, indicating it is the solution region. Since the line is dashed, it represents a non-inclusive inequality.

**Options:**

- ⦿ \(2x + 7y \leq 7\)
- ⃝ \(2x + 7y < 7\)
- ⃝ \(2x + 7y > 7\)
- ⃝ \(2x + 7y \geq 7\)
Transcribed Image Text:**Question:** 2. The shaded region of the graph represents which inequality? **Graph Explanation:** The graph shows a coordinate plane with a dashed line. The line has a negative slope, crossing the y-axis at (0, 1) and the x-axis at (3.5, 0). The region below the dashed line is shaded, indicating it is the solution region. Since the line is dashed, it represents a non-inclusive inequality. **Options:** - ⦿ \(2x + 7y \leq 7\) - ⃝ \(2x + 7y < 7\) - ⃝ \(2x + 7y > 7\) - ⃝ \(2x + 7y \geq 7\)
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