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iraph the inequality. y<-3x+4

iraph the inequality. y<-3x+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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How do I graph this? what are the points in the graph

To graph the inequality \( y \leq -3x + 4 \), we begin by examining the provided graph: 1. **Axes and Grid:** The graph is plotted on a coordinate plane with both the x-axis and y-axis marked at regular intervals. The x-values range from -10 to 10, and the y-values range from -10 to 10, each unit being distinctly marked. 2. **Line Representation:** The inequality \( y \leq -3x + 4 \) is represented by a solid line, which indicates that points on the line itself are included in the solution set. The line crosses the y-axis at the point (0, 4). 3. **Shaded Region:** The area above the line is shaded, denoting the region where \( y \) is greater than \( -3x + 4 \). Since the inequality is \( \leq \), we shade below the line, which is the region where the inequality holds true. 4. **Intersection and Origin:** There is an emphasis on the origin (0,0) with a cross symbol, indicating it as a reference point. 5. **Tool Icons:** To the right of the graph, there are several tool icons that seem to allow modifications or annotations to the graph, such as a drawing utensil, an eraser, graph reset options, and help. The graph effectively demonstrates how to plot an inequality by identifying the boundary line and appropriate shaded region that satisfies the inequality statement.
Transcribed Image Text:To graph the inequality \( y \leq -3x + 4 \), we begin by examining the provided graph: 1. **Axes and Grid:** The graph is plotted on a coordinate plane with both the x-axis and y-axis marked at regular intervals. The x-values range from -10 to 10, and the y-values range from -10 to 10, each unit being distinctly marked. 2. **Line Representation:** The inequality \( y \leq -3x + 4 \) is represented by a solid line, which indicates that points on the line itself are included in the solution set. The line crosses the y-axis at the point (0, 4). 3. **Shaded Region:** The area above the line is shaded, denoting the region where \( y \) is greater than \( -3x + 4 \). Since the inequality is \( \leq \), we shade below the line, which is the region where the inequality holds true. 4. **Intersection and Origin:** There is an emphasis on the origin (0,0) with a cross symbol, indicating it as a reference point. 5. **Tool Icons:** To the right of the graph, there are several tool icons that seem to allow modifications or annotations to the graph, such as a drawing utensil, an eraser, graph reset options, and help. The graph effectively demonstrates how to plot an inequality by identifying the boundary line and appropriate shaded region that satisfies the inequality statement.
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