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Linear inequalities are graphically represented on Cartesian plane by a
- a)negative full space
- b)closed half space
- c)open half space
- d)positive full space
- e)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Linear inequalities are graphically represented on Cartesian plane by ...
The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.
Most Upvoted Answer
Linear inequalities are graphically represented on Cartesian plane by ...
Explanation:
Graphical representation of linear inequalities on Cartesian plane is done by plotting the points that satisfy the inequality and shading the region where the solution lies. The shaded region is usually a half-plane or a full-plane, depending on the type of inequality.
Closed half-space:
A closed half-space is a region of the plane where the solution includes the boundary line. It is represented by shading the region above or below the boundary line, depending on the inequality. A closed half-space is represented by a solid line.
Example:
Consider the inequality y ≤ 2x + 3. To graph this inequality, we first plot the boundary line y = 2x + 3. This line passes through the point (0, 3) and (1, 5).
Next, we choose a test point not on the line, say (0, 0), and check if it satisfies the inequality. Substituting x = 0 and y = 0 in the inequality, we get 0 ≤ 2(0) + 3, which is true. Hence, the solution lies below the line.
Therefore, we shade the region below the line and include the boundary line, which gives us a closed half-space.
The correct answer is option B, closed half-space.
Graphical representation of linear inequalities on Cartesian plane is done by plotting the points that satisfy the inequality and shading the region where the solution lies. The shaded region is usually a half-plane or a full-plane, depending on the type of inequality.
Closed half-space:
A closed half-space is a region of the plane where the solution includes the boundary line. It is represented by shading the region above or below the boundary line, depending on the inequality. A closed half-space is represented by a solid line.
Example:
Consider the inequality y ≤ 2x + 3. To graph this inequality, we first plot the boundary line y = 2x + 3. This line passes through the point (0, 3) and (1, 5).
Next, we choose a test point not on the line, say (0, 0), and check if it satisfies the inequality. Substituting x = 0 and y = 0 in the inequality, we get 0 ≤ 2(0) + 3, which is true. Hence, the solution lies below the line.
Therefore, we shade the region below the line and include the boundary line, which gives us a closed half-space.
The correct answer is option B, closed half-space.
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Community Answer
Linear inequalities are graphically represented on Cartesian plane by ...
B is correct.
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Linear inequalities are graphically represented on Cartesian plane by aa)negative full spaceb)closed half spacec)open half spaced)positive full spacee)Correct answer is option 'B'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Linear inequalities are graphically represented on Cartesian plane by aa)negative full spaceb)closed half spacec)open half spaced)positive full spacee)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Linear inequalities are graphically represented on Cartesian plane by aa)negative full spaceb)closed half spacec)open half spaced)positive full spacee)Correct answer is option 'B'. Can you explain this answer?.
Linear inequalities are graphically represented on Cartesian plane by aa)negative full spaceb)closed half spacec)open half spaced)positive full spacee)Correct answer is option 'B'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Linear inequalities are graphically represented on Cartesian plane by aa)negative full spaceb)closed half spacec)open half spaced)positive full spacee)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Linear inequalities are graphically represented on Cartesian plane by aa)negative full spaceb)closed half spacec)open half spaced)positive full spacee)Correct answer is option 'B'. Can you explain this answer?.
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