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 ≥). It represents a region of the coordinate plane.

Front

How do you graph a linear inequality?

Back

1. Start by graphing the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). 2. Choose a test point not on the line to determine which side of the line to shade. 3. Shade the region that satisfies the inequality.

Front

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

Back

'≤' means 'less than or equal to'. It indicates that the values on the left can be less than or equal to the value on the right.

Front

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

Back

'≥' means 'greater than or equal to'. It indicates that the values on the left can be greater than or equal to the value on the right.

Front

What is slope-intercept form of a linear equation?

Back

Front

How do you convert a linear inequality to slope-intercept form?

Back

Front

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

Back

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

Front

What does it mean if a point lies above the line in a graph of a linear inequality?

Back

Front

What does it mean if a point lies below the line in a graph of a linear inequality?

Back

Front

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

Back

You can use a test point (often (0,0) if it's not on the line) to see if it satisfies the inequality. If it does, shade the side of the line that includes the test point.