Grade 9 · Math · Algebra 1

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

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Graph and write a two-variable inequality

Grade 9 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

1.
Milo wants y alone in -3y > 6x - 9, with the same graph. Which inequality does that?
- y < -2x + 3
- y > -2x + 3
- y < -2x - 9
- y < -2x - 3
2.
Noah wants y alone in 6x + 3y < 12, with the same graph. Which inequality does that?
- y > -2x + 4
- y < -2x + 4
- y < -2x + 12
- y < 2x + 4
3.
Pia wants y alone in 5x + 5y ≥ 15, with the same graph. Which inequality does that?
- y ≥ -x + 15
- y ≤ -x + 3
- y ≥ -x + 3
- y ≥ x + 3
Read this first
Boundary rows
x y
0 4
1 2
2 0
3 -2
4.
Ren fills a table for the boundary line. The line is dashed and the point (0, 0) is shaded. Which inequality fits?
- y < 2x + 4
- y < -2x + 4
- y > -2x + 4
- y ≤ -2x + 4
5.
Tala fills a table for the boundary line. The line is solid and the point (0, 0) is shaded. Which inequality fits?
- y ≥ 3x
- y ≥ 3x - 3
- y > 3x - 3
- y ≤ 3x - 3
6.
Zee fills a table for the boundary line. The line is solid and the point (1, 9) is shaded. Which inequality fits?
- y ≤ 3x + 2
- y ≥ 3x + 5
- y ≥ 3x + 2
- y > 3x + 2
7.
Ari fills a table for the boundary line. The line is dashed and the point (0, 0) is shaded. Which inequality fits?
- y < 2x + 7
- y < -2x + 7
- y ≤ -2x + 7
- y > -2x + 7
Esme plots points with whole-number x and y, both at least 0. How many points make x + y ≤ 6 true?
Jun plots points with whole-number x and y, both at least 0. How many points make 3x + 2y < 13 true?
Kira plots points with whole-number x and y, both at least 0. How many points make x + 2y ≤ 8 true?

x	y
0	4
1	2
2	0
3	-2

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

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