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Worksheets›Algebra 1›Linear functions & sequences›Graphs of linear inequalities

Graphs of Linear Inequalities Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

Algebra 1CCSS HSA.REI.D.12Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: Whole-number slopes

  1. 1.Write the inequality shown by the graph.xy−6−4−20246−6−4−20246
  2. 2.Write the inequality shown by the graph.xy−6−4−20246−6−4−20246
  3. 3.Write the inequality shown by the graph.xy−6−4−20246−6−4−20246
  4. 4.Write the inequality shown by the graph.xy−6−4−20246−6−4−20246
  5. 5.Write the inequality shown by the graph.xy−6−4−20246−6−4−20246
  6. 6.Write the inequality shown by the graph.xy−6−4−20246−6−4−20246
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

First write the equation of the boundary line. A dashed line means the points on it aren't solutions, so the sign is < or >; a solid line means they are, so the sign is ≤ or ≥. Shading above the line means y is greater than the line; shading below means y is less. For a vertical line, shading to the right means x is greater.

EasyWrite the inequality shown by the graph.xy−6−4−20246−6−4−20246Whole-number slopesMediumWrite the inequality shown by the graph.xy−6−4−20246−6−4−20246Fraction slopesHardWrite the inequality shown by the graph.xy−6−4−20246−6−4−20246Horizontal and vertical boundaries

How to solve it: a worked example

Write the inequality shown by each graph.

  1. StartWrite the inequality shown by the graph.xy−6−4−20246−6−4−20246
  2. The boundary liney = −2x − 1
  3. A dashed line means < or >y < −2x − 1
  4. Shaded below the line: y is lessy < −2x − 1
  5. Answery < −2x − 1

Common mistakes to watch for

  • Using ≤ or ≥ for a dashed boundary line.
  • Choosing the sign from the slope instead of from the shaded side.
  • Writing a vertical boundary as y = k instead of x = k.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

Related worksheets

Slope-intercept formParallel and perpendicular linesEvaluating functionsArithmetic and geometric sequencesStandard and point-slope form

FAQ

How can a test point confirm which side is shaded?

Pick a point not on the line, usually (0, 0), and substitute it into your inequality. If it makes the inequality true, that point's side should be shaded.

Does "above" always mean y is greater?

Yes, once the inequality is solved for y. If it is written another way, such as 2x − y > 3, solve for y first; that flips the sign: y < 2x − 3.

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix graphs of linear inequalities with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.