Graphing Inequalities in 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

How do you graph the inequality y < x - 3?

Back

To graph y < x - 3, first graph the line y = x - 3 as a dashed line (indicating that points on the line are not included). Then shade the area below the line, which represents all the points where y is less than x - 3.

Front

What does the dashed line represent in graphing inequalities?

Back

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

Front

What does the solid line represent in graphing inequalities?

Back

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

Front

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

Back

To determine if a point is a solution to an inequality, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is part of the solution set.

Front

Which inequality corresponds to the graph with a shaded area above the line y = 3/4x + 5?

Back

The inequality that corresponds to the graph is y > 3/4x + 5.

Front

What is the solution set of an inequality?

Back

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

Front

How can you tell if a point is NOT part of the solution set?

Back

A point is NOT part of the solution set if, when substituted into the inequality, it does not satisfy the inequality.

Front

What is the significance of the inequality symbol in y ≤ 3/4x + 5?

Back

The symbol '≤' indicates that the line y = 3/4x + 5 is included in the solution set, meaning points on the line satisfy the inequality.

Front

What does it mean if an inequality is written as y ≥ 2x - 1?

Back

It means that the graph includes the line y = 2x - 1 (solid line) and the area above the line, representing all points where y is greater than or equal to 2x - 1.