5.12 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 (>, <, ≥, ≤) instead of an equal sign.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≥ or ≤) or a dashed line (for > or <). Then, shade the region that satisfies the inequality.

Front

What does the shaded region represent in the graph of a linear inequality?

Back

The shaded region represents all the solutions to the inequality, indicating the set of points that satisfy the inequality.

Front

What is the significance of a solid line in graphing inequalities?

Back

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

Front

What does a dashed line indicate in graphing inequalities?

Back

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

Front

How can 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, the point is a solution.

Front

What is the solution set of the inequality y < -2x - 5?

Back

The solution set includes all points (x, y) that lie below the line y = -2x - 5.

Front

Which ordered pair is a solution to the inequality y ≥ -x + 1?

Back

The ordered pair (2, 1) is a solution because it satisfies the inequality when substituted.

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, it is included in the solution set if the line is solid (≥ or ≤) and not included if the line is dashed (> or <).

Front

How do you identify a point that is NOT part of the solution set?

Back

A point that does not satisfy the inequality when substituted into it is not part of the solution set.