Graphs 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 in a linear inequality?

Back

The symbol '≥' indicates that the values of the variable can be equal to or greater than a certain number.

Front

What does the symbol '<' indicate in a linear inequality?

Back

The symbol '<' indicates that the values of the variable must be less than a certain number.

Front

How do you represent the solution set of a linear inequality graphically?

Back

The solution set of a linear inequality is represented graphically by a shaded region on one side of a boundary line, which is either solid or dashed depending on the inequality.

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

How do you determine which side of the line to shade when graphing a linear inequality?

Back

To determine which side to shade, you can test a point not on the line (often (0,0)) in the inequality. If the inequality holds true, shade the side containing that point.

Front

Back

Front

Which of the following points is NOT part of the solution set for the inequality @@y eq -3@@? (0, 0), (-10, -10), (-1, 5), (5, 20)

Back

The point (-10, -10) is NOT part of the solution set for the inequality @@y eq -3@@.

Front

What is the graph of the inequality @@x eq 2@@?

Back

Front

How do you write the inequality for a line that has a slope of 2 and passes through the point (0, 1) and is above the line?

Back