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What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥) instead of an equal sign.

Tags

CCSS.7.EE.B.4B

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How do you graph a linear inequality?

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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.

Tags

CCSS.HSA.REI.D.12

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 (x, y) that satisfy all inequalities in the system simultaneously.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

A solid line indicates that points on the line are included in the solution set (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

Tags

CCSS.HSA.REI.D.12

Front

How can you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution to a linear inequality, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is part of the solution set.

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What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more linear inequalities that are considered together. The solution is the intersection of the solution sets of each inequality.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean for a point to be 'not part of the solution set'?

Back

A point is 'not part of the solution set' if it does not satisfy at least one of the inequalities in the system.

Tags

CCSS.HSA.REI.D.12

Front

How do you write a linear equation from a word problem involving costs?

Back

To write a linear equation from a word problem involving costs, identify the variables representing the quantities, set up an equation based on the relationships described in the problem, and include the total cost as a constant.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients in a linear equation represent the rate of change or the slope of the line, indicating how much the dependent variable changes for a unit change in the independent variable.

Tags

CCSS.HSF.LE.B.5

Front

What is the graphical representation of a system of linear inequalities?

Back

The graphical representation of a system of linear inequalities is the shaded region where all the inequalities overlap, showing all possible solutions.

Tags

CCSS.HSA.REI.D.12