Linear Inequalities

Front

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 ≥.

Front

How do you represent a linear inequality graphically?

Back

A linear inequality is represented graphically by a region of the coordinate plane that is either above or below a line, depending on the inequality sign.

Front

What does the inequality symbol '>' indicate when graphing?

Back

The symbol '>' indicates that the line is not included in the solution set, so a dashed line is used to represent the boundary.

Front

What does the inequality symbol '<' indicate when graphing?

Back

The symbol '<' indicates that the line is not included in the solution set, so a dashed line is used to represent the boundary.

Front

What does the inequality symbol '≥' indicate when graphing?

Back

The symbol '≥' indicates that the line is included in the solution set, so a solid line is used to represent the boundary.

Front

What does the inequality symbol '≤' indicate when graphing?

Back

The symbol '≤' indicates that the line is included in the solution set, so a solid line is used to represent the boundary.

Front

How do you determine which side of the line to shade when graphing a linear inequality?

Back

To determine which side to shade, you can test a point not on the line (usually (0,0) if it's not on the line) to see if it satisfies the inequality.

Front

What is the difference between a solid line and a dashed line in the context of linear 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 <).

Front

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

Back

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.

Front

How do you convert a linear equation into a linear inequality?

Back

To convert a linear equation into a linear inequality, replace the equality sign (=) with an inequality sign (<, >, ≤, or ≥).