Back to Graph linear inequalities — Problem 2 · Task Set 53

HSA.REI.D.12 Tutor Intake — Graphing Linear Inequalities

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Grade 9·8 problems·~12 min·Common Core Math - HS Algebra·standard·hsa-rei-d-12

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Concepts

After drawing the boundary line for $y \geq 2x - 3$ , a student needs
to decide which side to shade.

They test the origin $(0, 0)$ : $0 \geq 2(0) - 3 \Rightarrow 0 \geq -3$ . True.

Which region should be shaded?

The side NOT containing the origin, because $0 \geq -3$ seems too easy to satisfy.

The side containing the origin, because the test point satisfies the inequality.

Both sides, since the inequality is non-strict ( $\geq$ ).

Neither side — the boundary line itself is the solution set.