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2x-y스7 2<+3y크3

2x-y스7 2<+3y크3

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.3: Parallel And Perpendicular Lines
Problem 45HP
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Graph the solution set of the compound inequality 

Title: Graphing Linear Inequalities **Graph Description:** The graph is a standard Cartesian coordinate plane. It includes a horizontal x-axis and a vertical y-axis, both ranging from -10 to 10. Each axis is marked at intervals of 1 unit. The grid lines create a series of squares that extend across the first, second, third, and fourth quadrants. **Linear Inequalities:** The following linear inequalities are provided for graphing: 1. \(2x - y \leq 7\) 2. \(2x + 3y \geq 3\) **Instructions for Graphing the Inequalities:** 1. **Graph the boundary line for \(2x - y = 7\):** - Convert the inequality to the equation \(y = 2x - 7\). - Plot the boundary line by finding the intercepts or using a table of values. - Since the inequality is \(\leq\), shade the region below the line, including the boundary line. 2. **Graph the boundary line for \(2x + 3y = 3\):** - Convert the inequality to the equation \(y = \frac{-2}{3}x + 1\). - Plot this boundary line as well. - Since the inequality is \(\geq\), shade the region above the line, including the boundary line. **Interpreting the Graph:** The solution to the system of inequalities is the overlapping region that satisfies both conditions. This area is where the shaded regions of both inequalities intersect. When plotting the graph on your coordinate plane, accurately shading and labeling the regions will help in understanding the solutions effectively.
Transcribed Image Text:Title: Graphing Linear Inequalities **Graph Description:** The graph is a standard Cartesian coordinate plane. It includes a horizontal x-axis and a vertical y-axis, both ranging from -10 to 10. Each axis is marked at intervals of 1 unit. The grid lines create a series of squares that extend across the first, second, third, and fourth quadrants. **Linear Inequalities:** The following linear inequalities are provided for graphing: 1. \(2x - y \leq 7\) 2. \(2x + 3y \geq 3\) **Instructions for Graphing the Inequalities:** 1. **Graph the boundary line for \(2x - y = 7\):** - Convert the inequality to the equation \(y = 2x - 7\). - Plot the boundary line by finding the intercepts or using a table of values. - Since the inequality is \(\leq\), shade the region below the line, including the boundary line. 2. **Graph the boundary line for \(2x + 3y = 3\):** - Convert the inequality to the equation \(y = \frac{-2}{3}x + 1\). - Plot this boundary line as well. - Since the inequality is \(\geq\), shade the region above the line, including the boundary line. **Interpreting the Graph:** The solution to the system of inequalities is the overlapping region that satisfies both conditions. This area is where the shaded regions of both inequalities intersect. When plotting the graph on your coordinate plane, accurately shading and labeling the regions will help in understanding the solutions effectively.
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