Back to Graph linear inequalities — Problem 2 · Task Set 54

Exercises: Graph Linear Inequalities and Systems

For each graphing problem, state: (1) whether the boundary is solid or dashed, (2) which test point you used, and (3) which half-plane is shaded. For systems, verify a point in the feasible region satisfies all inequalities.

Grade 9·18 problems·~40 min·Common Core Math - HS Algebra·standard·hsa-rei-d-12

Work through problems with immediate feedback

Recall / Warm-Up

To determine which half-plane to shade for $3x + 2y \leq 12$ , a student substitutes $(0, 0)$ :
$3(0) + 2(0) = 0 \leq 12$ . True.

What does this tell the student?

Shade the half-plane that does NOT contain the origin.

Shade the half-plane that contains the origin.

The boundary passes through the origin, so use a different test point.

The inequality has no solution.