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 boundary line. Use a solid line for ≤ or ≥ and a dashed line for < or >. Then shade the appropriate region based on the inequality.

Front

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

Back

The symbol '≥' indicates that the values of the inequality include the boundary line, meaning the solutions are greater than or equal to the value.

Front

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

Back

The symbol '<' indicates that the values of the inequality do not include the boundary line, meaning the solutions are strictly less than the value.

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

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

What is the significance of the y-intercept in the context of linear inequalities?

Back

The y-intercept is the point where the line crosses the y-axis and is crucial for graphing the inequality, as it helps to establish the boundary line.

Front

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

Back

To identify the correct graph, first graph the boundary line based on the inequality symbol, then shade the region that satisfies the inequality.

Front

What does it mean if a point lies above the boundary line in a graph of a linear inequality?

Back

If a point lies above the boundary line in a graph of a linear inequality, it means that the point satisfies the inequality (for inequalities of the form y > mx + b or y ≥ mx + b).

Front

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

Back

The slope indicates the steepness of the line and the direction of the inequality. A positive slope means the line rises from left to right, while a negative slope means it falls.