Solid horizontal line y = 3, shade below

Dashed horizontal line y = 3, shade above

Solid vertical line x = -2, shade right

Solid horizontal line y = 5, shade below

Dashed horizontal line y = -7, shade above

Solid vertical line x = -3, shade right

Solid vertical line x = 3, shade right

Dashed horizontal line y = 6, shade above

Worksheets · Algebra 2

Algebra 2 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.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Graphing Linear Inequalities Date Period Graph each inequality, or answer as asked. Graph $2 y \geq - 3 x + 12$ Graph $y \leq 3$ Is $(- 3, - 7)$ a solution of $y < - 3 x - 6$ ? Graph $2 y < 3 x - 8$ Graph $y > 3$ Is $(2, - 1)$ a solution of $y > 3 x + 4$ ? Graph $3 y < 2 x + 9$ Graph $x \geq - 2$ Is $(1, 8)$ a solution of $y > x - 4$ ? Graph $- 2 y > - 8 x + 2$ Graph $y \leq 5$ Is $(4, - 4)$ a solution of $y > 5 x - 7$ ? Graph $- 3 y < - 5 x - 9$ Graph $y > - 7$ Is $(2, 0)$ a solution of $y < - x - 2$ ? Graph $2 y > - 5 x + 10$ Graph $x \geq - 3$ Is $(- 3, 6)$ a solution of $y \geq x$ ? Graph $2 y < 5 x + 10$ Graph $x \geq 3$ 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.

Graph $2 y \geq - 3 x + 12$
Graph $y \leq 3$
Is $(- 3, - 7)$ a solution of $y < - 3 x - 6$ ?
Graph $2 y < 3 x - 8$
Graph $y > 3$
Is $(2, - 1)$ a solution of $y > 3 x + 4$ ?
Graph $3 y < 2 x + 9$
Graph $x \geq - 2$
Is $(1, 8)$ a solution of $y > x - 4$ ?
Graph $- 2 y > - 8 x + 2$
Graph $y \leq 5$
Is $(4, - 4)$ a solution of $y > 5 x - 7$ ?
Graph $- 3 y < - 5 x - 9$
Graph $y > - 7$
Is $(2, 0)$ a solution of $y < - x - 2$ ?
Graph $2 y > - 5 x + 10$
Graph $x \geq - 3$
Is $(- 3, 6)$ a solution of $y \geq x$ ?
Graph $2 y < 5 x + 10$
Graph $x \geq 3$



Sigma Prep · sigmaprep.io/worksheets Name Graphing Linear InequalitiesAnswer keyVersion 1 Date Period Graph each inequality, or answer as asked. Graph $2 y \geq - 3 x + 12$ solid line, shade above Graph $y \leq 3$ Solid horizontal line $y = 3$ , shade below Is $(- 3, - 7)$ a solution of $y < - 3 x - 6$ ?Yes: $- 7 < 3$ is true Graph $2 y < 3 x - 8$ dashed line, shade below Graph $y > 3$ Dashed horizontal line $y = 3$ , shade above Is $(2, - 1)$ a solution of $y > 3 x + 4$ ?No: $- 1 > 10$ is false Graph $3 y < 2 x + 9$ dashed line, shade below Graph $x \geq - 2$ Solid vertical line $x = - 2$ , shade right Is $(1, 8)$ a solution of $y > x - 4$ ?Yes: $8 > - 3$ is true Graph $- 2 y > - 8 x + 2$ dashed line, shade below Graph $y \leq 5$ Solid horizontal line $y = 5$ , shade below Is $(4, - 4)$ a solution of $y > 5 x - 7$ ?No: $- 4 > 13$ is false Graph $- 3 y < - 5 x - 9$ dashed line, shade above Graph $y > - 7$ Dashed horizontal line $y = - 7$ , shade above Is $(2, 0)$ a solution of $y < - x - 2$ ?No: $0 < - 4$ is false Graph $2 y > - 5 x + 10$ dashed line, shade above Graph $x \geq - 3$ Solid vertical line $x = - 3$ , shade right Is $(- 3, 6)$ a solution of $y \geq x$ ?Yes: $6 \geq - 3$ is true Graph $2 y < 5 x + 10$ dashed line, shade below Graph $x \geq 3$ Solid vertical line $x = 3$ , shade right 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.

Graph $2 y \geq - 3 x + 12$ solid line, shade above
Graph $y \leq 3$ Solid horizontal line $y = 3$ , shade below
Is $(- 3, - 7)$ a solution of $y < - 3 x - 6$ ?Yes: $- 7 < 3$ is true
Graph $2 y < 3 x - 8$ dashed line, shade below
Graph $y > 3$ Dashed horizontal line $y = 3$ , shade above
Is $(2, - 1)$ a solution of $y > 3 x + 4$ ?No: $- 1 > 10$ is false
Graph $3 y < 2 x + 9$ dashed line, shade below
Graph $x \geq - 2$ Solid vertical line $x = - 2$ , shade right
Is $(1, 8)$ a solution of $y > x - 4$ ?Yes: $8 > - 3$ is true
Graph $- 2 y > - 8 x + 2$ dashed line, shade below
Graph $y \leq 5$ Solid horizontal line $y = 5$ , shade below
Is $(4, - 4)$ a solution of $y > 5 x - 7$ ?No: $- 4 > 13$ is false
Graph $- 3 y < - 5 x - 9$ dashed line, shade above
Graph $y > - 7$ Dashed horizontal line $y = - 7$ , shade above
Is $(2, 0)$ a solution of $y < - x - 2$ ?No: $0 < - 4$ is false
Graph $2 y > - 5 x + 10$ dashed line, shade above
Graph $x \geq - 3$ Solid vertical line $x = - 3$ , shade right
Is $(- 3, 6)$ a solution of $y \geq x$ ?Yes: $6 \geq - 3$ is true
Graph $2 y < 5 x + 10$ dashed line, shade below
Graph $x \geq 3$ Solid vertical line $x = 3$ , shade right

How to do these

Graph $y > 2 x - 3$

Draw y = 2x - 3, dashed because it is a strict inequality.
Test the origin: 0 > -3 is true.
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 $y > 3 x - 5$ → dashed line, shade above
A fraction slope: Graph $y \geq \frac{2}{3} x + 5$ → 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 $y > 3 x + 4$ ? → 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 2 is usually taken around 10th or 11th 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.

Algebra 2 graphing linear inequalities worksheet

Select your difficulty

Graphing Linear Inequalities

Graphing Linear InequalitiesAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these graphing linear inequalities worksheets free?+

Do the graphing linear inequalities worksheets come with an answer key?+

Are these graphing linear inequalities worksheets printable?+

What grade are these graphing linear inequalities worksheets for?+

Can I get a different version of the same graphing linear inequalities worksheet?+

Is this a free alternative to Kuta Software for graphing linear inequalities?+

Can I choose how hard the graphing linear inequalities questions are?+

What kinds of question are on a graphing linear inequalities worksheet?+

What do students get wrong with graphing linear inequalities?+