What is the significance of the boundary line in a linear inequality?

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not. It is crucial for determining the feasible region.

What does it mean for a system of inequalities to have an infinite number of solutions?

A system of inequalities has an infinite number of solutions when the feasible region is unbounded or when the inequalities overlap significantly.

How do you write an inequality from a graph?

To write an inequality from a graph, identify the slope and y-intercept of the boundary line, and determine whether the line is solid or dashed to decide on the inequality symbol.

What is the slope-intercept form of a linear equation?

The slope-intercept form of a linear equation is given by $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

What does the term 'solution set' refer to in linear inequalities?

The solution set is the collection of all points that satisfy the system of inequalities, represented graphically as the feasible region.

How can you identify a point that is not a solution to a system of inequalities?

A point that does not satisfy at least one of the inequalities in the system is not a solution. You can check this by substituting the point into the inequalities.

What is the role of test points in graphing inequalities?

Test points are used to determine which side of the boundary line to shade. If the test point satisfies the inequality, shade the region containing that point.

What is the importance of understanding linear inequalities in real-world applications?

Understanding linear inequalities is crucial for solving problems involving constraints, such as budgeting, resource allocation, and optimization in various fields.

5A Graphing systems of Linear Inequalities

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA.REI.D.12, 8.EE.B.6, 8.F.A.3

Standards-aligned

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FLASHCARD QUESTION

Front

What is a linear inequality?

Back

FLASHCARD QUESTION

Front

What does it mean for a system of linear inequalities to have no solution?

Back

A system of linear inequalities has no solution when the inequalities represent parallel lines that do not intersect.

Tags

CCSS.HSA.REI.D.12

FLASHCARD QUESTION

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane divided by a boundary line, which can be solid (inclusive) or dashed (exclusive).

Tags

CCSS.HSA.REI.D.12

FLASHCARD QUESTION

Front

How do 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.

FLASHCARD QUESTION

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

Tags

CCSS.HSA.REI.D.12

FLASHCARD QUESTION

Front

What does the term 'feasible region' refer to in the context of linear inequalities?

Back

The feasible region is the area on the graph where all the solutions to the system of inequalities exist. It is the intersection of all half-planes.

Tags

CCSS.HSA.REI.D.12

FLASHCARD QUESTION

Front

How can you graph a system of linear inequalities?

Back

To graph a system of linear inequalities, first graph each inequality as a line, then shade the appropriate half-plane for each inequality. The overlapping shaded area represents the solution set.

Tags

CCSS.HSA.REI.D.12

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