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Graph the inequality y > 5 -x - 3. 3

Graph the inequality y > 5 -x - 3. 3

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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Question
**Graphing Linear Inequalities** **Objective:** Learn how to graph the inequality \( y > \frac{5}{3}x - 3 \). ### Step-by-Step Instructions: #### 1. Examine the Given Inequality We need to graph the inequality \( y > \frac{5}{3}x - 3 \). #### 2. Identify the Slope and Intercept The inequality is in slope-intercept form \( y = mx + b \), where: - \( m \) (slope) is \(\frac{5}{3} \) - \( b \) (y-intercept) is -3 #### 3. Plot the Y-Intercept Locate -3 on the y-axis and plot a point. #### 4. Use the Slope to Find Another Point Slope ( \( m = \frac{5}{3} \) ) means rise over run. From the intercept point: - Rise 5 units up. - Run 3 units to the right. Plot this second point. #### 5. Draw the Boundary Line Since the inequality is strictly greater than ( \( y > \) ), we use a dashed line: - Draw a dashed line through the two points. #### 6. Determine the Shading Direction For \( y > \frac{5}{3}x - 3 \), shade above the dashed line. ### Graph Details: - **Axes Labels:** The x-axis and y-axis range from -5 to 5 in both directions. - **Dashed Line:** Represents the boundary where \( y = \frac{5}{3}x - 3 \). (Note: Use dashed to show the inequality does not include the boundary line). - **Shaded Area:** Above the line where \( y \) values are greater than \( \frac{5}{3}x - 3 \). This detailed approach ensures your graph correctly represents the inequality, aiding in visual understanding.
Transcribed Image Text:**Graphing Linear Inequalities** **Objective:** Learn how to graph the inequality \( y > \frac{5}{3}x - 3 \). ### Step-by-Step Instructions: #### 1. Examine the Given Inequality We need to graph the inequality \( y > \frac{5}{3}x - 3 \). #### 2. Identify the Slope and Intercept The inequality is in slope-intercept form \( y = mx + b \), where: - \( m \) (slope) is \(\frac{5}{3} \) - \( b \) (y-intercept) is -3 #### 3. Plot the Y-Intercept Locate -3 on the y-axis and plot a point. #### 4. Use the Slope to Find Another Point Slope ( \( m = \frac{5}{3} \) ) means rise over run. From the intercept point: - Rise 5 units up. - Run 3 units to the right. Plot this second point. #### 5. Draw the Boundary Line Since the inequality is strictly greater than ( \( y > \) ), we use a dashed line: - Draw a dashed line through the two points. #### 6. Determine the Shading Direction For \( y > \frac{5}{3}x - 3 \), shade above the dashed line. ### Graph Details: - **Axes Labels:** The x-axis and y-axis range from -5 to 5 in both directions. - **Dashed Line:** Represents the boundary where \( y = \frac{5}{3}x - 3 \). (Note: Use dashed to show the inequality does not include the boundary line). - **Shaded Area:** Above the line where \( y \) values are greater than \( \frac{5}{3}x - 3 \). This detailed approach ensures your graph correctly represents the inequality, aiding in visual understanding.
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