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 (>, <, ≥, ≤).

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shaded on one side of a boundary line.

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

Front

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

Back

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

Front

What does shading above a line in a graph of an inequality indicate?

Back

Shading above the line indicates that the solutions to the inequality are greater than the line (y > mx + b).

Front

What does shading below a line in a graph of an inequality indicate?

Back

Shading below the line indicates that the solutions to the inequality are less than the line (y < mx + b).

Front

How do you graph the inequality y < 2x + 3?

Back

Graph the line y = 2x + 3 with a dashed line and shade below the line.

Front

What is the significance of the inequality symbol in graphing?

Back

The inequality symbol determines whether the line is solid or dashed and indicates the direction of shading.

Front

What is the solution set of a linear inequality?

Back

The solution set is the collection of all points (x, y) that satisfy the inequality.

Front

How can you check if a point lies in the solution set of an inequality?

Back

Substitute the point's coordinates into the inequality. If the statement is true, the point lies in the solution set.