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 such as <, >, ≤, or ≥.

Front

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

Back

The symbol '>' means 'greater than'. For example, in the inequality y > 2x + 2, y is greater than the value of 2x + 2.

Front

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

Back

The symbol '<' means 'less than'. For example, in the inequality y < -2x - 2, y is less than the value of -2x - 2.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. For example, in the inequality x ≥ -3, x is greater than or equal to -3.

Front

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

Back

The symbol '≤' means 'less than or equal to'. For example, in the inequality y ≤ 2, y is less than or equal to 2.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, depending on the inequality symbol. Then shade the appropriate region based on the inequality.

Front

What is the difference between a dashed line and a solid line in graphing inequalities?

Back

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

Front

How do you determine which side of the line to shade when graphing an inequality?

Back

To determine which side to shade, pick a test point not on the line (usually (0,0) if it's not on the line) and substitute it into the inequality. If the inequality holds true, shade that side; if not, shade the opposite side.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, represented graphically as a shaded region on the graph.

Front

How can you write an inequality from a graph?

Back

To write an inequality from a graph, identify the boundary line and determine if it is dashed or solid. Then, find the slope and y-intercept, and use the appropriate inequality symbol based on the shaded region.