Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality symbol.

Front

What does a dashed line indicate in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set (used for < or >).

Front

What does a solid line indicate in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (used for ≤ or ≥).

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.

Front

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

Back

To determine which side to shade, pick a test point not on the line (usually (0,0)), substitute it into the inequality, and shade the side that makes the inequality true.

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than and does not include the boundary, while '≥' means greater than or equal to and includes the boundary.

Front

What is the difference between '<' and '≤'?

Back

'<' means less than and does not include the boundary, while '≤' means less than or equal to and includes the boundary.

Front

What is a boundary line in the context of linear inequalities?

Back

A boundary line is the line that represents the equation of the linear inequality, separating the solution set from the non-solution set.

Front

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

Back

To check if a point is a solution, substitute the coordinates of the point into the inequality and see if the statement is true.