CCSS.Math.Content.HSA-REI.D.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.
Common Core State Standards for Mathematics
What this standard means
Students need to graph a linear inequality by first graphing its boundary line, choosing solid or dashed, then shading the correct half-plane. They also need to graph several inequalities on the same coordinate plane and identify the overlapping region that satisfies all conditions.
Mastery looks like accurate boundary lines, correct shading, and clear use of test points or inequality reasoning. Students often mix up dashed and solid lines, shade the wrong side, or think the answer is one point instead of a region. Systems get tricky when the overlap is small, unbounded, or empty.
Ways to teach it
- Have students use colored pencils to graph three inequalities on grid paper, then label the overlap as the solution region.
- Ask students to explain how they know whether to shade above or below the line y = 2x - 3.
- Give four small graphs and have students circle the one that matches x + y < 6 and y ≥ 1.
- Use a snack stand budget problem with two constraints, then graph the possible combinations of drinks and chips.
Plan a lesson for CCSS.Math.Content.HSA-REI.D.12
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Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
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