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 ≤ represent in an inequality?

Back

The symbol ≤ means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol < represent in an inequality?

Back

The symbol < means 'less than', indicating that the value on the left must be strictly less than the value on the right.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a line. Use a solid line for ≤ or ≥ and a dotted line for < or >. Then shade the appropriate region based on the inequality.

Front

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

Back

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

Front

If the inequality is y < 3, what is the correct graph?

Back

The graph will have a dotted horizontal line at y = 3, with the area below the line shaded.

Front

What does it mean to shade above the line in a graph of an inequality?

Back

Shading above the line indicates that the solutions to the inequality are all the points where the y-value is greater than the y-value of the line.

Front

What does it mean to shade below the line in a graph of an inequality?

Back

Shading below the line indicates that the solutions to the inequality are all the points where the y-value is less than the y-value of the line.

Front

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

Back

You can test a point not on the line (often (0,0) if it's not on the line) in the inequality. If the inequality holds true, shade the side of the line that includes that point.

Front

What is the inequality for the relationship shown if the graph shows a line at y = 100 with a solid line?

Back

The inequality is y ≤ 100.