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, so a solid line is used.

Front

What does the symbol '>' indicate when graphing?

Back

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

Front

How do you determine if a point is part of the solution set for a linear inequality?

Back

To determine if a point is part of the solution set, substitute the point's coordinates into the inequality. If the inequality holds true, the point is part of the solution set.

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 >).

Front

Back

A dashed line is used because the inequality does not include the boundary line.

Front

What does shading above the line indicate in a graph of a linear inequality?

Back

Shading above the line indicates that the solution set includes all points where the y-value is greater than the value of the linear expression.

Front

What does shading below the line indicate in a graph of a linear inequality?

Back

Shading below the line indicates that the solution set includes all points where the y-value is less than the value of the linear expression.

Front

How can you check if a point lies in the shaded region of a graph?

Back

To check if a point lies in the shaded region, substitute the point's coordinates into the inequality. If the inequality is true, the point is in the shaded region.

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.