Graphing linear inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

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 a dashed line indicate in the graph of a linear inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set of the inequality.

Front

What does a solid line indicate in the graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set of the inequality.

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

Front

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

Back

The shaded region represents all the possible solutions to the inequality.

Front

What is the difference between 'greater than' and 'greater than or equal to' in linear inequalities?

Back

'Greater than' (>) means the boundary line is dashed, while 'greater than or equal to' (≥) means the boundary line is solid.

Front

What is the difference between 'less than' and 'less than or equal to' in linear inequalities?

Back

'Less than' (<) means the boundary line is dashed, while 'less than or equal to' (≤) means the boundary line is solid.

Front

How do you identify the correct graph for a given linear inequality?

Back

To identify the correct graph, first determine the type of line (dashed or solid) based on the inequality symbol, then check which side of the line is shaded according to the inequality.

Front

What is the role of the slope in graphing linear inequalities?

Back

The slope determines the steepness of the line and the direction it rises or falls, which is essential for accurately graphing the linear equation.