Graphing Inequalities
Graph linear inequalities
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In This Topic (1 lessons)
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 You'll 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.