Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
To graph the inequality [tex]\( y \geq x - 2 \)[/tex], follow these detailed steps:
1. Graph the boundary line [tex]\( y = x - 2 \)[/tex]:
- This boundary is a straight line.
- Since the inequality is [tex]\( \geq \)[/tex], this line will be solid, indicating that points on the line satisfy the inequality.
2. Find the y-intercept and x-intercept of the line [tex]\( y = x - 2 \)[/tex]:
- Y-intercept: Set [tex]\( x = 0 \)[/tex]. Then,
[tex]\[ y = 0 - 2 \][/tex]
[tex]\[ y = -2 \][/tex]
So, the y-intercept is [tex]\( (0, -2) \)[/tex].
- X-intercept: Set [tex]\( y = 0 \)[/tex]. Then,
[tex]\[ 0 = x - 2 \][/tex]
[tex]\[ x = 2 \][/tex]
So, the x-intercept is [tex]\( (2, 0) \)[/tex].
3. Plot the boundary line using the intercepts:
- Start by plotting the points [tex]\( (0, -2) \)[/tex] and [tex]\( (2, 0) \)[/tex].
- Draw a straight line through these points, extending in both directions. This line represents the equation [tex]\( y = x - 2 \)[/tex].
4. Determine which side of the line to shade for the inequality [tex]\( y \geq x - 2 \)[/tex]:
- Choose a test point not on the line to determine which side to shade. A convenient point to use is [tex]\( (0, 0) \)[/tex].
- Substitute [tex]\( (0, 0) \)[/tex] into the inequality:
[tex]\[ 0 \geq 0 - 2 \][/tex]
[tex]\[ 0 \geq -2 \][/tex]
This inequality is true, so the point [tex]\( (0, 0) \)[/tex] satisfies the inequality. Thus, the area containing [tex]\( (0, 0) \)[/tex] should be shaded.
5. Shade the correct region:
- Since [tex]\( y \geq x - 2 \)[/tex] is satisfied by the test point [tex]\( (0, 0) \)[/tex], shade the region above the boundary line [tex]\( y = x - 2 \)[/tex].
6. Finalize your graph:
- Draw the boundary line [tex]\( y = x - 2 \)[/tex] as a solid line to show that points on the line are included in the inequality.
- Shade the entire region above this line to represent all points where [tex]\( y \geq x - 2 \)[/tex].
### Summary of Steps:
1. Draw a solid line for [tex]\( y = x - 2 \)[/tex].
2. Shade the region above the line to represent [tex]\( y \geq x - 2 \)[/tex].
The resultant graph will have a solid line passing through the points [tex]\( (0, -2) \)[/tex] and [tex]\( (2, 0) \)[/tex], with the area above this line shaded, indicating that all points in this region satisfy the inequality [tex]\( y \geq x - 2 \)[/tex].
1. Graph the boundary line [tex]\( y = x - 2 \)[/tex]:
- This boundary is a straight line.
- Since the inequality is [tex]\( \geq \)[/tex], this line will be solid, indicating that points on the line satisfy the inequality.
2. Find the y-intercept and x-intercept of the line [tex]\( y = x - 2 \)[/tex]:
- Y-intercept: Set [tex]\( x = 0 \)[/tex]. Then,
[tex]\[ y = 0 - 2 \][/tex]
[tex]\[ y = -2 \][/tex]
So, the y-intercept is [tex]\( (0, -2) \)[/tex].
- X-intercept: Set [tex]\( y = 0 \)[/tex]. Then,
[tex]\[ 0 = x - 2 \][/tex]
[tex]\[ x = 2 \][/tex]
So, the x-intercept is [tex]\( (2, 0) \)[/tex].
3. Plot the boundary line using the intercepts:
- Start by plotting the points [tex]\( (0, -2) \)[/tex] and [tex]\( (2, 0) \)[/tex].
- Draw a straight line through these points, extending in both directions. This line represents the equation [tex]\( y = x - 2 \)[/tex].
4. Determine which side of the line to shade for the inequality [tex]\( y \geq x - 2 \)[/tex]:
- Choose a test point not on the line to determine which side to shade. A convenient point to use is [tex]\( (0, 0) \)[/tex].
- Substitute [tex]\( (0, 0) \)[/tex] into the inequality:
[tex]\[ 0 \geq 0 - 2 \][/tex]
[tex]\[ 0 \geq -2 \][/tex]
This inequality is true, so the point [tex]\( (0, 0) \)[/tex] satisfies the inequality. Thus, the area containing [tex]\( (0, 0) \)[/tex] should be shaded.
5. Shade the correct region:
- Since [tex]\( y \geq x - 2 \)[/tex] is satisfied by the test point [tex]\( (0, 0) \)[/tex], shade the region above the boundary line [tex]\( y = x - 2 \)[/tex].
6. Finalize your graph:
- Draw the boundary line [tex]\( y = x - 2 \)[/tex] as a solid line to show that points on the line are included in the inequality.
- Shade the entire region above this line to represent all points where [tex]\( y \geq x - 2 \)[/tex].
### Summary of Steps:
1. Draw a solid line for [tex]\( y = x - 2 \)[/tex].
2. Shade the region above the line to represent [tex]\( y \geq x - 2 \)[/tex].
The resultant graph will have a solid line passing through the points [tex]\( (0, -2) \)[/tex] and [tex]\( (2, 0) \)[/tex], with the area above this line shaded, indicating that all points in this region satisfy the inequality [tex]\( y \geq x - 2 \)[/tex].
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
