Grade 9 · Math · Algebra 1

9th grade Graph and write a two-variable inequality worksheet

6 printable versionsOn Level10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Graph and write a two-variable inequality

Grade 9 Math Worksheet

NameDate

Circle the best answer.

1.
Jun draws a graph. The line is solid and the part below it is shaded. Which inequality does it show?
- y ≤ 2x + 4
- y < -2x + 4
- y ≥ -2x + 4
- y ≤ -2x + 4
2.
Kira plots a graph. The line is dashed and the part below it is shaded. Which inequality does it show?
- y < 2x + 2
- y > 2x + 2
- y ≤ 2x + 2
- y < 2x + 4
3.
Luz sketches a graph. The line is solid and the part above it is shaded. Which inequality does it show?
- y ≤ -3x + 2
- y > -3x + 2
- y ≥ -3x + 2
- y ≥ -3x - 1
4.
Milo draws a graph. The line is dashed and the part below it is shaded. Which inequality does it show?
- y > -3x + 5
- y ≤ -3x + 5
- y < 3x + 5
- y < -3x + 5
5.
Pia buys x stickers at $2 and y bookmarks at $3. Pia can spend at most $30. Which inequality fits?
- 2x + 3y ≤ 30
- 2x + 3y < 30
- 2x + 3y ≥ 30
- 3x + 2y ≤ 30
6.
Noah loads x backpacks at 3 kg and y tents at 5 kg into a trailer. The trailer carries at most 24 kg. Which inequality fits?
- 3x + 5y ≤ 24
- 3x + 5y ≥ 24
- 5x + 3y ≤ 24
- 3x + 5y < 24
7.
Luz wins x small prizes worth 5 points and y big prizes worth 10 points. Luz needs at least 60 points. Which inequality fits?
- 5x + 10y > 60
- 5x + 10y ≤ 60
- 10x + 5y ≥ 60
- 5x + 10y ≥ 60
8.
Ari graphs 2x + 5y ≥ 10. Which description of the graph is right?
- Dashed line through (0, 2) and (5, 0); shade the side that does not have (0, 0)
- Solid line through (0, 5) and (2, 0); shade the side that does not have (0, 0)
- Solid line through (0, 2) and (5, 0); shade the side that has (0, 0)
- Solid line through (0, 2) and (5, 0); shade the side that does not have (0, 0)
9.
Bo graphs x > 2 on a grid. Which description of the graph is right?
- Dashed horizontal line at y = 2; shade above
- Solid vertical line at x = 2; shade right
- Dashed vertical line at x = 2; shade left
- Dashed vertical line at x = 2; shade right
10.
Jun graphs x < -3 on a grid. Which description of the graph is right?
- Dashed vertical line at x = -3; shade right
- Dashed horizontal line at y = -3; shade below
- Dashed vertical line at x = -3; shade left
- Solid vertical line at x = -3; shade left

9th grade Graph and write a two-variable inequality worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Graph and write a two-variable inequality. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can tell whether a point is a solution by putting its row beside the rule's row at the same x.
I can graph an inequality: solid or dashed, shade the side, and test (0, 0) when the line is in standard form.
I can write the inequality from a graph, a table, or a story with a limit.

Standard: A-REI.D.12, A-CED.A.3, A-CED.A.2

Words to know

boundary line: The line y = mx + b where the inequality changes from true to false.

solid / dashed: Solid keeps the points on the line (≤ or ≥); dashed leaves them out (< or >).

half-plane: All the points on one side of the boundary line.

test point: A point you try in the inequality to see which side is shaded.

at most / at least: At most is ≤; at least is ≥. Both include the limit.

more than / fewer than: More than is >; fewer than is <. Both leave the limit out.

Common mistakes

Your child counted points on a dashed line as solutions.

Your child picked a point on the wrong side of the line.

Your child tested the point with its numbers in the wrong order.

What to say

Ask: does < or > include the points on the line itself?

Ask: is the point's output bigger or smaller than the rule's output at the same x?

Ask: which number goes across, and which goes up?

Questions parents ask

What is the most common mistake with graph and write a two-variable inequality?

Your child counted points on a dashed line as solutions.

How can I help my child with graph and write a two-variable inequality?

Ask: does < or > include the points on the line itself?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 1

See all Algebra 1

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records