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The graph of a system of inequalities is shown. 10 8 10 -8 -6 -4 -2 8 10 -8 -10 Create the system of inequalities that is represented by the graph. 4. 2.

The graph of a system of inequalities is shown. 10 8 10 -8 -6 -4 -2 8 10 -8 -10 Create the system of inequalities that is represented by the graph. 4. 2.

Algebra and Trigonometry (6th Edition)
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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The graph of a system of inequalities is shown.

​Create the system of inequalities that is represented by the graph.



 

The graph of a system of inequalities is shown. **Graph Description:** The graph includes two lines, each representing a different linear inequality. The coordinate plane is divided into four quadrants with both the x-axis and y-axis ranging from -10 to 10. The shaded region indicates the solution to the system of inequalities. 1. **Solid Line:** - This line passes through the points (-8, -2) and (8, 6), suggesting a linear equation. - It appears to be in the form \( y = \frac{1}{2}x + 2 \). - This line is a border for the shaded region, indicating that the inequality is inclusive (≤ or ≥). 2. **Dashed Line:** - This horizontal line correlates to \( y = -3 \). - The shading is below this line, suggesting the inequality \( y < -3 \) (not inclusive). **Shaded Region:** - The region is below the horizontal dashed line and below or on the solid line. This represents the solution set for the system of inequalities. **Task:** Create the system of inequalities represented by this graph. Consider the lines and the shaded region to express the system in mathematical terms. **System of Inequalities:** - \( y \leq \frac{1}{2}x + 2 \) - \( y < -3 \)
Transcribed Image Text:The graph of a system of inequalities is shown. **Graph Description:** The graph includes two lines, each representing a different linear inequality. The coordinate plane is divided into four quadrants with both the x-axis and y-axis ranging from -10 to 10. The shaded region indicates the solution to the system of inequalities. 1. **Solid Line:** - This line passes through the points (-8, -2) and (8, 6), suggesting a linear equation. - It appears to be in the form \( y = \frac{1}{2}x + 2 \). - This line is a border for the shaded region, indicating that the inequality is inclusive (≤ or ≥). 2. **Dashed Line:** - This horizontal line correlates to \( y = -3 \). - The shading is below this line, suggesting the inequality \( y < -3 \) (not inclusive). **Shaded Region:** - The region is below the horizontal dashed line and below or on the solid line. This represents the solution set for the system of inequalities. **Task:** Create the system of inequalities represented by this graph. Consider the lines and the shaded region to express the system in mathematical terms. **System of Inequalities:** - \( y \leq \frac{1}{2}x + 2 \) - \( y < -3 \)
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