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 (like <, >, ≤, or ≥) and involves two variables, typically x and y.

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is any number greater than 3.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. For example, y < 5 means y is any number less than 5.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 2 means x is any number greater than or equal to 2.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. For example, y ≤ 4 means y is any number less than or equal to 4.

Front

How do you graph the inequality y > 3?

Back

To graph y > 3, draw a dashed horizontal line at y = 3 and shade the area above the line.

Front

How do you graph the inequality y < -1?

Back

To graph y < -1, draw a dashed horizontal line at y = -1 and shade the area below the line.

Front

What type of line is used for the inequalities < and >?

Back

A dashed or dotted line is used for the inequalities < and > to indicate that the points on the line are not included in the solution.

Front

What type of line is used for the inequalities ≤ and ≥?

Back

A solid line is used for the inequalities ≤ and ≥ to indicate that the points on the line are included in the solution.

Front

Is the point (1, 2) a solution to the inequality y < x + 1?

Back

No, because when you substitute x = 1, y must be less than 2, but (1, 2) gives y = 2.