Worksheets · Algebra 1

Graphing linear inequalities worksheet for Algebra 1

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

Also taught in Pre-Algebra and Algebra 2, each at its own level and with its own examples.

Not quite the one you need? Same words, different skill:

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Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Linear Inequalities

Date Period

Graph each inequality, or answer as asked.

  1. Graph a linear inequality

    Graph 2y≥−3x+12−10−10−5−5551010
  2. Graph −2y≤x+2−10−10−5−5551010
  3. Graph −2y<6x+6−10−10−5−5551010
  4. Graph −3y≥−4x−15−10−10−5−5551010
  5. Graph 2y<7x+10−10−10−5−5551010
  6. Graph 3y≤−4x−9−10−10−5−5551010
  7. Graph −3y<x−9−10−10−5−5551010

  1. Graph inequalities in one variable

    Graph y<−7−10−10−5−5551010
  2. Graph x≤4−10−10−5−5551010
  3. Graph x≥−1−10−10−5−5551010
  4. Graph y≥2−10−10−5−5551010
  5. Graph x>7−10−10−5−5551010
  6. Graph y≤−2−10−10−5−5551010
  7. Graph y>−2−10−10−5−5551010

  1. Test a point in an inequality

    Is (0,−9) a solution of y>−3x−4?
  2. Is (−3,5) a solution of y≤3x+5?
  3. Is (−2,4) a solution of y<−5x+4?
  4. Is (−4,−2) a solution of y<−5x−6?
  5. Is (−3,−7) a solution of y<−x+5?
  6. Is (−3,−7) a solution of y≥x−6?

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, or answer as asked.

  1. Graph a linear inequality

    Graph 2y≥−3x+12−10−10−5−5510105solid line, shade above
  2. Graph −2y≤x+2−10−10−5−5551010solid line, shade above
  3. Graph −2y<6x+6−10−10−5−5551010dashed line, shade above
  4. Graph −3y≥−4x−15−10−10−5551010−5solid line, shade below
  5. Graph 2y<7x+10−10−10−5−5551010dashed line, shade below
  6. Graph 3y≤−4x−9−10−10−5−5551010solid line, shade below
  7. Graph −3y<x−9−10−10−5−5551010dashed line, shade above

  1. Graph inequalities in one variable

    Graph y<−7−10−10−5−5551010Dashed horizontal line y=−7, shade below
  2. Graph x≤4−10−10−5−5551010Solid vertical line x=4, shade left
  3. Graph x≥−1−10−5510−10−5510Solid vertical line x=−1, shade right
  4. Graph y≥2−10−10−5−5551010Solid horizontal line y=2, shade above
  5. Graph x>7−10−10−5−5551010Dashed vertical line x=7, shade right
  6. Graph y≤−2−10−10−5−5551010Solid horizontal line y=−2, shade below
  7. Graph y>−2−10−10−5−5551010Dashed horizontal line y=−2, shade above

  1. Test a point in an inequality

    Is (0,−9) a solution of y>−3x−4?No: −9>−4 is false
  2. Is (−3,5) a solution of y≤3x+5?No: 5≤−4 is false
  3. Is (−2,4) a solution of y<−5x+4?Yes: 4<14 is true
  4. Is (−4,−2) a solution of y<−5x−6?Yes: −2<14 is true
  5. Is (−3,−7) a solution of y<−x+5?Yes: −7<8 is true
  6. Is (−3,−7) a solution of y≥x−6?Yes: −7≥−9 is true

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.

What you can put on this worksheet

One inequality, shaded
Graph y>3x−5 → dashed line, shade above
A fraction slope
Graph y≥23x+5 → solid line, shade above
A horizontal or vertical boundary
Graph y>6 → Dashed horizontal line y=6, shade above
Is the point a solution?
Is (0,1) a solution of y>3x+4? → No: 1>4 is false

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.

You pick from 4: one inequality, shaded, a fraction slope, a horizontal or vertical boundary and is the point a solution?. Tick as many as you want and set how many of each, or let it spread them evenly.

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.