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 ≥). It represents a region of the coordinate plane.

Front

How do you graph a linear inequality?

Back

1. Start by graphing the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). 2. Choose a test point not on the line to determine which side of the line to shade. 3. Shade the region that satisfies the inequality.

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the values of the variable can be less than or equal to a certain number.

Front

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

Back

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

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

Front

How do you write the inequality for a graph with a solid line at y = -2x - 2?

Back

Front

How do you write the inequality for a graph with a dashed line at y = 2x + 2?

Back

Front

What does it mean if a point (x, y) is a solution to a linear inequality?

Back

It means that when the coordinates of the point are substituted into the inequality, the statement is true.

Front

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

Back

Substitute the x and y values of the point into the inequality. If the resulting statement is true, then the point is a solution.

Front

What is the solution set of a linear inequality?

Back

The solution set is the set of all points (x, y) that satisfy the inequality, represented graphically as a shaded region on the coordinate plane.