Graphing Systems of Linear Inequalities (Part 3)

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Mathematics
•
8th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a linear inequality?
Back
A linear inequality is a mathematical expression that relates a linear function to a value using inequality symbols (such as <, >, ≤, or ≥) instead of an equal sign.
2.
FLASHCARD QUESTION
Front
How do you graph a linear inequality?
Back
To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, shade the region that satisfies the inequality.
3.
FLASHCARD QUESTION
Front
What does it mean for a point to be a solution to a system of inequalities?
Back
A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.
4.
FLASHCARD QUESTION
Front
What is the difference between a solid line and a dashed line in graphing inequalities?
Back
A solid line indicates that the points on the line are included in the solution (for ≤ or ≥), while a dashed line indicates that the points on the line are not included (for < or >).
5.
FLASHCARD QUESTION
Front
How can you determine if a point is a solution to a system of inequalities?
Back
To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.
6.
FLASHCARD QUESTION
Front
What is the significance of the intersection of shaded regions in a graph of inequalities?
Back
The intersection of shaded regions represents the set of solutions that satisfy all inequalities in the system.
7.
FLASHCARD QUESTION
Front
What does the notation 'y ≤ 2x - 1' represent?
Back
This notation represents a linear inequality where the values of y are less than or equal to the values of the linear function 2x - 1.
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