NY Next Generation Math AI-A.REI.12
The Standard
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students graph a linear inequality in two variables as a half-plane and distinguish solid from dashed boundaries. They find solutions to systems by intersecting the corresponding half-planes.
What Mastery Looks Like
- The student graphs each boundary line, shades the correct side, and identifies the overlap for a system. Test points confirm both the shading and whether boundary points belong.
Common Misconceptions
- Students may shade the wrong side, use a solid boundary for a strict inequality, or treat a boundary line as the whole solution. They may ignore one inequality when naming the system's solutions.
How to Assess It
- Ask students to graph y greater than 2x minus 1 and y less than or equal to 5, then test one boundary and one overlap point.
Lesson moves
Ways to Teach It
Layer transparent half-plane sheets over a coordinate grid to reveal the intersection of two inequalities.
Ask students how the inequality symbol determines whether boundary points count as solutions.
Play shading check by testing coordinate cards against student-drawn half-planes and systems.
Model a production plan with two resource limits and interpret the feasible overlap on a graph.
Keep exploring
Related Standards
- AII-A.REI.7.b
Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
- AI-A.REI.10
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
- AI-A.REI.6.a
Solve systems of linear equations in two variables both algebraically and graphically.
- NY-8.EE.8.a
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersect...
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