Worksheets · Algebra 1

Graphing linear inequalities worksheet

Two decisions per question: whether the boundary line is dashed or solid, and which side gets shaded. The answer key shows both.

Select your difficulty

Pick more than one for a sheet that mixes them.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Linear Inequalities

Date Period

Graph each inequality.

  1. Graph 2y≥−3x+12-10-10-5-55510100
  2. Graph 2y>3x+12-10-10-5-55510100
  3. Graph 2y>−4x−8-10-10-5-55510100
  4. Graph −2y≤x+2-10-10-5-55510100
  5. Graph −2y<3x+6-10-10-5-55510100
  6. Graph −2y<5x−10-10-10-5-55510100
  7. Graph −2y≤−7x−12-10-10-5-55510100
  8. Graph 3y≥x−18-10-10-5-55510100
  9. Graph −3y<−5x−9-10-10-5-55510100
  10. Graph 3y>−5x−12-10-10-5-55510100
  11. Graph 2y>−3x+10-10-10-5-55510100
  12. Graph −2y>x+12-10-10-5-55510100
  13. Graph −2y<3x-10-10-5-55510100
  14. Graph 2y<5x+10-10-10-5-55510100
  15. Graph 2y≥4x+6-10-10-5-55510100
  16. Graph −2y≥7x+4-10-10-5-55510100
  17. Graph −2y>3x+8-10-10-5-55510100
  18. Graph −3y<2x+18-10-10-5-55510100
  19. Graph −2y>x−8-10-10-5-55510100
  20. Graph −2y≤−x+8-10-10-5-55510100

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Linear InequalitiesAnswer keyVersion 1

Date Period

Graph each inequality.

  1. Graph 2y≥−3x+12-10-10-5-55510100solid line, shade above
  2. Graph 2y>3x+12-10-10-5-55510100dashed line, shade above
  3. Graph 2y>−4x−8-10-10-5-55510100dashed line, shade above
  4. Graph −2y≤x+2-10-10-5-55510100solid line, shade above
  5. Graph −2y<3x+6-10-10-5-55510100dashed line, shade above
  6. Graph −2y<5x−10-10-10-5-55510100dashed line, shade above
  7. Graph −2y≤−7x−12-10-10-5-55510100solid line, shade above
  8. Graph 3y≥x−18-10-10-5-55510100solid line, shade above
  9. Graph −3y<−5x−9-10-10-5-55510100dashed line, shade above
  10. Graph 3y>−5x−12-10-10-5-55510100dashed line, shade above
  11. Graph 2y>−3x+10-10-10-5-55510100dashed line, shade above
  12. Graph −2y>x+12-10-10-5-55510100dashed line, shade below
  13. Graph −2y<3x-10-10-5-55510100dashed line, shade above
  14. Graph 2y<5x+10-10-10-5-55510100dashed line, shade below
  15. Graph 2y≥4x+6-10-10-5-55510100solid line, shade above
  16. Graph −2y≥7x+4-10-10-5-55510100solid line, shade below
  17. Graph −2y>3x+8-10-10-5-55510100dashed line, shade below
  18. Graph −3y<2x+18-10-10-5-55510100dashed line, shade above
  19. Graph −2y>x−8-10-10-5-55510100dashed line, shade below
  20. Graph −2y≤−x+8-10-10-5-55510100solid line, shade above

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Graph y>2x−3

  1. Draw y = 2x - 3, dashed because it is a strict inequality.
  2. Test the origin: 0 > -3 is true.
  3. So shade the side containing the origin.

The answer is dashed line, shade above.

Where students go wrong

Shading the wrong side by guessing. Test a point, and the origin is the easiest one unless the line passes through it. Greater-than does not always mean above once the line is rearranged.

Also called shading inequalities, half planes or graphing inequalities on a grid.

Questions about these worksheets

Yes. Every graphing linear inequalities sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the graphing linear inequalities questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Shading the wrong side by guessing. Test a point, and the origin is the easiest one unless the line passes through it. Greater-than does not always mean above once the line is rearranged.