Linear Inequalities and Graphing Lines

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 value on the left is greater than the value on the right.

Front

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

Back

The symbol '<' indicates that the value on the left is less than the value on the right.

Front

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

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

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

Back

The symbol '≤' indicates that the value on the left is less than or equal to the value on the right.

Front

How do you represent a linear inequality graphically?

Back

A linear inequality is represented graphically by a line and a shaded region. The line can be solid or dashed depending on whether the inequality includes equality.

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 (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

When graphing the inequality y < 2x + 3, where do you shade?

Back

You shade below the line because the inequality symbol is '<'.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all ordered pairs (x, y) that satisfy the inequality.

Front

How do you determine if an ordered pair is a solution to a linear inequality?

Back

To determine if an ordered pair is a solution, substitute the x and y values into the inequality and check if the statement is true.