Graphing Inequalities
Graph linear inequalities
Learning Objectives
Discussion Starters
Differentiation Ideas
Presentation Mode
lessons (1)
Graphing inequalities shows regions of solutions rather than single lines or curves. Linear inequalities in two variables create half-planes, and systems of inequalities create regions bounded by multiple constraints. These skills apply to optimization problems and real-world constraint modeling.
What Students Will Learn
- Graph linear inequalities in two variables
- Identify solution regions with shading
- Graph systems of linear inequalities
- Write inequalities from graphs
- Apply to real-world constraint problems
Frequently Asked Questions
How do I know which side to shade?
Test a point not on the line (usually the origin). If the point satisfies the inequality, shade that side. If not, shade the other side.
When do I use a dashed vs solid line?
Use a solid line for ≤ or ≥ (boundary included). Use a dashed line for < or > (boundary not included).
What is a feasible region?
The feasible region is where all inequalities in a system are satisfied simultaneously. It is the overlap of all individual solution regions.