Choose the Boundary Style and Shaded Side

Supplied materials

• Paper or a browser scratch area; a calculator is optional unless rounding is requested.
• Supplied teaching case: How should y<2x+2 be represented on a coordinate plane? Candidate answers: (A) Dashed boundary line; shade above it (B) Dashed boundary line; shade below it (C) Solid boundary line; shade above it (D) Solid boundary line; shade below it.
• Independent check inputs: How should y<2x+3 be represented on a coordinate plane? Candidate answers: (A) Dashed boundary line; shade above it (B) Dashed boundary line; shade below it (C) Solid boundary line; shade above it (D) Solid boundary line; shade below it.

Learn the idea

A mathematical plan can require simultaneous equalities or inequalities. The feasible set contains inputs satisfying all constraints, and a linear objective asks which allowed choice gives the greatest or least modeled value. A strict linear inequality excludes its equality line, represented by a dashed boundary. Output values below the line satisfy a less-than comparison when the inequality is solved for y.

Here is the method on the supplied teaching case. The strict sign excludes equality, so the boundary is dashed. Smaller y-values lie below the line y=2x+2. Test any convenient off-line point to check the side.

A solid line includes equality, so it would misrepresent a strict sign. The shading depends on the solved comparison; use an off-boundary test point when unsure rather than relying on a sketch.

1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
3. Solve the independent check with its changed inputs before revealing feedback.
4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Check your reasoning

Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.

Take it further

Changed-input task: How should y<2x+9 be represented on a coordinate plane? Candidate answers: (A) Dashed boundary line; shade above it (B) Dashed boundary line; shade below it (C) Solid boundary line; shade above it (D) Solid boundary line; shade below it. Show the mathematical reason, not only the selected answer. Expected result: Dashed boundary line; shade below it. The strict sign excludes equality, so the boundary is dashed. Smaller y-values lie below the line y=2x+9. Test any convenient off-line point to check the side.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.