Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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The image features two coordinate plane graphs labeled C and D. Each graph contains a system of inequalities represented by dashed lines, along with shaded regions indicating the solution sets. ### Graph C: - **Axes**: The x-axis and y-axis both extend from -10 to 10. - **Lines**: - The first line runs diagonally from the top left to the bottom right. This line intersects the y-axis at approximately -7 and the x-axis at approximately 7. - The second line is a curve that appears to be parabolic, opening upwards and intersecting the x-axis close to the origin, curving towards the right. - **Shading**: The area to the left of the parabolic curve, above the diagonal line, is shaded in gray. This indicates the solution region for the system of inequalities. ### Graph D: - **Axes**: The x-axis and y-axis both extend from -10 to 10. - **Lines**: - The first line is similar to the diagonal line in Graph C, running from top left to bottom right, intersecting the y-axis and x-axis at around the same coordinates as Graph C. - The second line is another upward-opening curve, intersecting the y-axis above the x-axis and curving towards the right. - **Shading**: The area to the right of the parabolic curve, below the diagonal line, is shaded in gray, representing the solution region for this system of inequalities. Both graphs demonstrate how different inequalities can define distinct solution regions on the coordinate plane.
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Transcribed Image Text:The image features two coordinate plane graphs labeled C and D. Each graph contains a system of inequalities represented by dashed lines, along with shaded regions indicating the solution sets. ### Graph C: - **Axes**: The x-axis and y-axis both extend from -10 to 10. - **Lines**: - The first line runs diagonally from the top left to the bottom right. This line intersects the y-axis at approximately -7 and the x-axis at approximately 7. - The second line is a curve that appears to be parabolic, opening upwards and intersecting the x-axis close to the origin, curving towards the right. - **Shading**: The area to the left of the parabolic curve, above the diagonal line, is shaded in gray. This indicates the solution region for the system of inequalities. ### Graph D: - **Axes**: The x-axis and y-axis both extend from -10 to 10. - **Lines**: - The first line is similar to the diagonal line in Graph C, running from top left to bottom right, intersecting the y-axis and x-axis at around the same coordinates as Graph C. - The second line is another upward-opening curve, intersecting the y-axis above the x-axis and curving towards the right. - **Shading**: The area to the right of the parabolic curve, below the diagonal line, is shaded in gray, representing the solution region for this system of inequalities. Both graphs demonstrate how different inequalities can define distinct solution regions on the coordinate plane.
**Graph the Solution Set of the System of Inequalities:** **Problem:** 13. Graph the solution set of the system of inequalities: \( y < -x + 8 \) \( y > 8x - 3 \) **Graph A Description:** - The graph shows a coordinate plane with a shaded region. - The line \( y = -x + 8 \) is represented as a dashed line with a negative slope, starting at the y-intercept (0, 8). - The area above this line is unshaded, while the area below the line is not highlighted, indicating that solutions do not satisfy the inequality \( y < -x + 8 \). **Graph B Description:** - The graph displays another coordinate plane with a different shaded region. - The line \( y = 8x - 3 \) is represented as a dashed line with a positive slope, starting at the y-intercept (0, -3). - The area below this line is not shaded, while the area above the line is shaded, indicating that solutions satisfy the inequality \( y > 8x - 3 \). In conclusion, the correct graph should show the overlapping region where both inequalities are satisfied, meaning where one shaded region overlaps with the other.
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Transcribed Image Text:**Graph the Solution Set of the System of Inequalities:** **Problem:** 13. Graph the solution set of the system of inequalities: \( y < -x + 8 \) \( y > 8x - 3 \) **Graph A Description:** - The graph shows a coordinate plane with a shaded region. - The line \( y = -x + 8 \) is represented as a dashed line with a negative slope, starting at the y-intercept (0, 8). - The area above this line is unshaded, while the area below the line is not highlighted, indicating that solutions do not satisfy the inequality \( y < -x + 8 \). **Graph B Description:** - The graph displays another coordinate plane with a different shaded region. - The line \( y = 8x - 3 \) is represented as a dashed line with a positive slope, starting at the y-intercept (0, -3). - The area below this line is not shaded, while the area above the line is shaded, indicating that solutions satisfy the inequality \( y > 8x - 3 \). In conclusion, the correct graph should show the overlapping region where both inequalities are satisfied, meaning where one shaded region overlaps with the other.
Expert Solution
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Step 1

Topic- System of inequalities

We are given ,y<-x+8

y>8x-3

in slope intercept form ,

y=mx+c

m=slope of line

c=y intercept

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