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4. Match the graph to the correct system of inequalities. 10 Y a. y< b. 2" -10 C. y > -I yS-+4 d. y y<-r+4

4. Match the graph to the correct system of inequalities. 10 Y a. y< b. 2" -10 C. y > -I yS-+4 d. y y<-r+4

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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**Matching Graphs to Inequalities** The task is to match each graph to the correct system of inequalities. There are four sets of inequalities provided, labeled as a, b, c, and d. Each graph displays shaded regions to represent the solutions to these inequalities. ### Inequality Systems: 1. **a.** - \( y \leq \frac{1}{2}x - 5 \) - \( y \leq -2x + 4 \) 2. **b.** - \( y \leq \frac{1}{2}x - 5 \) - \( y \geq -2x + 4 \) 3. **c.** - \( y \geq \frac{1}{2}x - 5 \) - \( y \geq -2x + 4 \) 4. **d.** - \( y \leq \frac{1}{2}x - 5 \) - \( y < -x + 4 \) ### Graph Explanations: 1. **Top Graph:** - **Lines:** - A green dashed line: \( y = \frac{1}{2}x - 5 \), shading below (consistent with \(\leq\)). - A purple line: \( y = -2x + 4 \), shading below (consistent with \(\leq\)). - **Shaded Intersection:** Indicates where both inequalities are satisfied. 2. **Second Graph (Bottom Left):** - **Lines:** - A green dashed line: \( y = \frac{1}{2}x - 5 \), shading below (consistent with \(\leq\)). - A purple line: \( y = -x + 4 \), shading below, but the line is dashed indicating \(<\). - **Shaded Intersection:** Region where both inequalities hold. 3. **Third Graph (Bottom Middle):** - **Lines:** - A green line: \( y = -2x + 4 \), shading above (consistent with \(\geq\)). - A purple line: \( y = \frac{1}{2}x - 5 \), shading above. - **Shaded Intersection:** Solutions for the system where both conditions meet. 4. **Fourth Graph (Bottom Right
Transcribed Image Text:**Matching Graphs to Inequalities** The task is to match each graph to the correct system of inequalities. There are four sets of inequalities provided, labeled as a, b, c, and d. Each graph displays shaded regions to represent the solutions to these inequalities. ### Inequality Systems: 1. **a.** - \( y \leq \frac{1}{2}x - 5 \) - \( y \leq -2x + 4 \) 2. **b.** - \( y \leq \frac{1}{2}x - 5 \) - \( y \geq -2x + 4 \) 3. **c.** - \( y \geq \frac{1}{2}x - 5 \) - \( y \geq -2x + 4 \) 4. **d.** - \( y \leq \frac{1}{2}x - 5 \) - \( y < -x + 4 \) ### Graph Explanations: 1. **Top Graph:** - **Lines:** - A green dashed line: \( y = \frac{1}{2}x - 5 \), shading below (consistent with \(\leq\)). - A purple line: \( y = -2x + 4 \), shading below (consistent with \(\leq\)). - **Shaded Intersection:** Indicates where both inequalities are satisfied. 2. **Second Graph (Bottom Left):** - **Lines:** - A green dashed line: \( y = \frac{1}{2}x - 5 \), shading below (consistent with \(\leq\)). - A purple line: \( y = -x + 4 \), shading below, but the line is dashed indicating \(<\). - **Shaded Intersection:** Region where both inequalities hold. 3. **Third Graph (Bottom Middle):** - **Lines:** - A green line: \( y = -2x + 4 \), shading above (consistent with \(\geq\)). - A purple line: \( y = \frac{1}{2}x - 5 \), shading above. - **Shaded Intersection:** Solutions for the system where both conditions meet. 4. **Fourth Graph (Bottom Right
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