Graphing Linear Inequalites

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 of the line to shade?

Back

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

Front

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

Back

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

Front

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

Back

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

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, dividing the coordinate plane into two regions.

Front

Can a linear inequality have more than one solution?

Back

Yes, a linear inequality typically has infinitely many solutions, represented by the shaded region on the graph.