Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates 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

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

Front

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

Back

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

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

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

Back

To determine which side to shade, choose a test point (often (0,0) if it's not on the line) and substitute it into the inequality. If the inequality holds true, shade the side of the line that includes the test point.

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. It is represented graphically as a shaded region on the coordinate plane.

Front

How do you write an inequality from a graph?

Back

To write an inequality from a graph, identify the boundary line and determine whether it is solid or dashed. Then, observe the shaded region to see if it represents values greater than or less than the line.

Front

Back

Front

Back