Graphing Linear Inequalities in Two Variables
I can graph a linear inequality in two variables and shade the correct side of the boundary.
The problem this sheet solves
They arrive with a rule: greater than means shade above. It is not wrong so much as conditional, and nobody tells them the condition — it holds only once the inequality is solved for y. Hand them 2x − y > 4 and the rule fires on the > and shades above, when the answer is below. This sheet teaches three moves in a fixed order — boundary, edge, side — and makes the TEST POINT the one that decides. A student who tests a point is right whether or not they remembered to solve for y first, which is exactly why it is the habit worth building. The Watch Out, the Reasoning item and the Error Analysis are all the same misconception in three costumes, and one practice item deliberately hands them a boundary through the origin so that (0, 0) settles nothing and they have to know why.
The key rule
Graph the boundary line first, then decide its edge and its side. A strict sign gives a dashed boundary, an inclusive sign a solid one. Then test any point off the boundary: if it comes out true, shade that point's side, and if false, the other.
Boundary, then edge, then side. Test a point rather than trusting the direction of the sign.
Watch out
The mistake: Reading 2x − y > 4 as a greater-than and shading ABOVE the boundary.
The fix: Solve for y first and the sign flips: −y > −2x + 4 becomes y < 2x − 4, so the answer is BELOW. Testing (0, 0) catches it in one line.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.