Graphing Inequalities with Two Variables

Front

What is an inequality in two variables?

Back

An inequality in two variables is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, or ≥) and involves two variables, typically x and y.

Front

What does the graph of an inequality represent?

Back

The graph of an inequality represents all the solutions that satisfy the inequality, showing the region of possible values for the variables.

Front

What is a boundary line in the context of graphing inequalities?

Back

A boundary line is the line that separates the graph into two regions, representing the solutions of the inequality. It can be solid (inclusive) or dashed (exclusive).

Front

What does a solid line indicate in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is ≤ or ≥.

Front

What does a dashed line indicate in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is < or >.

Front

What is a half-plane in the context of graphing inequalities?

Back

A half-plane is one of the two regions created by the boundary line, representing all the solutions to the inequality on one side of the line.

Front

How do you determine which half-plane to shade when graphing an inequality?

Back

To determine which half-plane to shade, you can test a point not on the boundary line (often the origin) in the inequality. If the inequality holds true, shade that half-plane.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all ordered pairs (x, y) that satisfy the inequality.

Front

How can you check if a point is part of the solution set for an inequality?

Back

To check if a point is part of the solution set, substitute the coordinates of the point into the inequality. If the inequality is true, the point is part of the solution set.

Front

What is the significance of the coordinates (3, 1) in relation to an inequality?

Back

The coordinates (3, 1) can be tested in an inequality to determine if they satisfy the condition. If they do not satisfy the inequality, they are not part of the solution set.