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 (e.g., <, >, ≤, ≥).

Front

What does the solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality.

Front

Are points on a solid boundary line part of the solution set?

Back

Yes, points on a solid boundary line are part of the solution set.

Front

Are points on a dashed boundary line part of the solution set?

Back

No, points on a dashed boundary line are NOT part of the solution set.

Front

How do 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 inequality holds true, the point is a solution.

Front

What does shading above a line indicate in a linear inequality?

Back

Shading above a line indicates that the solutions are greater than the line's equation.

Front

What does shading below a line indicate in a linear inequality?

Back

Shading below a line indicates that the solutions are less than the line's equation.

Front

What is the significance of the inequality symbol in determining the type of line (solid or dashed)?

Back

If the inequality symbol includes 'or equal to' (≤ or ≥), the line is solid. If it does not ( < or >), the line is dashed.

Front

How can you tell if a point is in the solution set of a linear inequality?

Back

A point is in the solution set if it lies in the shaded region of the graph.

Front

What is the graphical representation of the inequality y < 2x + 3?

Back

The graph will have a dashed line for y = 2x + 3 and shading below the line.