Graphing Linear Inequalities and Systems of 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 line is solid and the region below the line is shaded, representing all points where the inequality holds true.

Front

What does the symbol '>' indicate when graphing?

Back

The symbol '>' indicates that the line is dotted (or dashed) and the region above the line is shaded, representing all points where the inequality holds true.

Front

How do you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the difference between a solid line and a dotted line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dotted line indicates that points on the line are not included ( < or >).

Front

What is a system of linear inequalities?

Back

A system of linear inequalities consists of two or more linear inequalities that are considered simultaneously, and the solution is the region where all inequalities overlap.

Front

How do you graph a system of linear inequalities?

Back

To graph a system of linear inequalities, graph each inequality on the same coordinate plane, using solid or dotted lines as appropriate, and shade the correct regions. The solution is where the shaded areas overlap.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line of a linear inequality, it is a solution if the line is solid (≤ or ≥) but not a solution if the line is dotted (< 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, represented graphically as a shaded region on the coordinate plane.

Front

How can you check if a point is not a solution to a system of inequalities?

Back

To check if a point is not a solution, substitute the point's coordinates into each inequality. If it fails to satisfy any of the inequalities, it is not a solution.