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 such as <, >, ≤, or ≥.

Front

What does the symbol ≤ indicate when graphing?

Back

The symbol ≤ indicates that the boundary line is included in the solution set, meaning points on the line are part of the solution.

Front

What does the symbol < indicate when graphing?

Back

The symbol < indicates that the boundary line is not included in the solution set, meaning points on the line are not part of the solution.

Front

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

Back

You shade above the line if the inequality symbol is > or ≥, and below the line if it is < or ≤.

Front

What type of line is used for inequalities with ≤ or ≥?

Back

A solid line is used for inequalities with ≤ or ≥ to indicate that points on the line are included in the solution set.

Front

What type of line is used for inequalities with < or >?

Back

A dashed line is used for inequalities with < or > to indicate that points on the line are not included in the solution set.

Front

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

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

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

What does it mean if a point lies in the shaded region of a graph of a linear inequality?

Back

If a point lies in the shaded region, it means that the point satisfies the inequality and is part of the solution set.

Front

Can a point on a dashed line be part of the solution set?

Back

No, a point on a dashed line cannot be part of the solution set because the dashed line indicates that those points are not included.