Linear Inequalities & Systems of Linear Inequalities

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•
Mathematics
•
6th - 9th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a linear inequality?
Back
A linear inequality is an inequality that involves a linear function, typically expressed in the form ax + by < c, ax + by ≤ c, ax + by > c, or ax + by ≥ c, where a, b, and c are constants.
2.
FLASHCARD QUESTION
Front
How do you determine if a point is a solution to a linear inequality?
Back
To determine if a point (x, y) is a solution to a linear inequality, substitute the x and y values into the inequality. If the inequality holds true, then the point is a solution.
3.
FLASHCARD QUESTION
Front
What is the difference between a solid line and a dashed line when graphing linear inequalities?
Back
A solid line indicates that the points on the line are included in the solution set (used for ≤ or ≥), while a dashed line indicates that the points on the line are not included (used for < or >).
4.
FLASHCARD QUESTION
Front
What does the solution set of a system of linear inequalities represent?
Back
The solution set of a system of linear inequalities represents all the points that satisfy all inequalities in the system simultaneously.
5.
FLASHCARD QUESTION
Front
How can you graph a linear inequality in two variables?
Back
To graph a linear inequality, first graph the corresponding linear equation as a line. Then, use a test point to determine which side of the line to shade, indicating the solution set.
6.
FLASHCARD QUESTION
Front
What is the significance of the boundary line in a linear inequality?
Back
The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not. The nature of the line (solid or dashed) indicates whether points on the line are included in the solution.
7.
FLASHCARD QUESTION
Front
What does the notation y ≥ -3 represent graphically?
Back
The notation y ≥ -3 represents all points on or above the horizontal line y = -3, including the line itself.
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