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 (>, <, ≥, ≤).

Front

What does the symbol '≥' mean in a linear inequality?

Back

'≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '>' mean in a linear inequality?

Back

'>' means 'greater than', indicating that the value on the left is strictly greater than the value on the right.

Front

What does the symbol '<' mean in a linear inequality?

Back

'<' means 'less than', indicating that the value on the left is strictly less than the value on the right.

Front

What does the symbol '≤' mean in a linear inequality?

Back

'≤' means 'less than or equal to', indicating that the value on the left is either less than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≥ or ≤) or a dashed line (for > or <). 2. Shade the region that satisfies the inequality.

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

Front

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

Back

Choose a test point (often (0,0) if it's not on the line). Substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

Front

What does it mean if a point is a solution to a linear inequality?

Back

A point is a solution if it satisfies the inequality when its coordinates are substituted into the inequality.

Front

If the inequality is y < 3x + 2, which side of the line will be shaded?

Back

The area below the line y = 3x + 2 will be shaded.