Mississippi Math FA.F.23
The Standard
With accuracy, graph the solutions to a linear inequality in two variables as a half-plane, and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes on the same Coordinate Plane. (A-REI.12) Construct graphs of linear inequalities and systems of linear inequalities without technology. Use appropriate strategies to verify points that may or may not belong to the solution set.
2025 Mississippi College- and Career-Readiness Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students draw boundary lines by hand. They shade each half-plane that satisfies an inequality and keep only the overlap for a system. They substitute points to check whether they belong.
What Mastery Looks Like
- A student plots both boundary lines accurately and shades only their overlap. They use solid lines when boundary points count and dashed lines when they do not. They check points inside, outside, and on a boundary by substitution.
Common Misconceptions
- Students may use a solid line for < or >. They may shade both half-planes instead of only their overlap, or shade the wrong side without testing a point. They may count a point on a dashed boundary as a solution.
How to Assess It
- On graph paper, graph y ≥ 2x − 1 and y < −x + 5 on the same axes. Shade the solution set, then use substitution to check (1, 1) and (2, 3).
Lesson moves
Ways to Teach It
On separate tracing-paper grids, graph and shade y ≥ x and y < 4 − x, then stack the grids to locate the overlap.
Show a dashed boundary for y ≤ 2x + 1 and ask, “Does (0, 1) count? What should change?”
Post y ≥ x and y < 4 − x; partners draw coordinate cards and earn a point only after checking both inequalities.
Plan a $40 snack order: graph 2x + 3y ≤ 40, x ≥ 0, and y ≥ 0 for $2 drinks and $3 sandwiches.
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Printable FA.F.23 Worksheet
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Related Standards
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Graph a system of two functions, f(x) and g(x), on the same Coordinate Plane by hand for simple cases, and with technology for complicated cases. Explain the re...
- FA.A.10
Graph the solution point of an equation and the solution set of an inequality in one variable on a horizontal number line. For inequalities, be able to interpre...
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