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 in a linear inequality?

Back

The symbol '>' indicates that the value on the left is greater than the value on the right, and it does not include the boundary line.

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, and it does not include the boundary line.

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, including the boundary line.

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, including the boundary line.

Front

How do you graph a linear inequality with a dashed line?

Back

You graph a linear inequality with a dashed line when the inequality symbol is '>' or '<', indicating that points on the line are not included in the solution.

Front

How do you graph a linear inequality with a solid line?

Back

You graph a linear inequality with a solid line when the inequality symbol is '≥' or '≤', indicating that points on the line are included in the solution.

Front

What is the shaded region in a graph of a linear inequality?

Back

The shaded region represents all the solutions to the inequality, showing where the inequality holds true.

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 into the inequality. If the inequality holds true, the point is a solution.

Front

What is the difference between a solution and a non-solution in the context of linear inequalities?

Back

A solution satisfies the inequality, meaning it lies in the shaded region, while a non-solution does not satisfy the inequality and lies outside the shaded region.