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 - Building Confidence

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Rule table for the boundary y = 2x - 3
x y
0 -3
1 -1
2 1
3 3
1.
Ari sorts points with a pencil. Which point is a solution of y > 2x - 3?
- (3, 2)
- (1, -5)
- (2, 3)
- (3, 3)
Rule table for the boundary y = -x + 5
x y
0 5
1 4
2 3
3 2
2.
Bo tests points on graph paper. Which point is a solution of y < -x + 5?
- (3, 4)
- (1, 2)
- (2, 3)
- (1, 6)
Rule table for the boundary y = -2x + 3
x y
0 3
1 1
2 -1
3 -3
3.
Jun marks points with a star sticker. Which point is a solution of y ≤ -2x + 3?
- (2, -3)
- (2, 5)
- (3, 2)
- (1, 4)
Boundary rule y = 2x + 1. Rows
x y
0 1
1 3
2 5
4.
Kira graphs for a poster. Which drawing shows y > 2x + 1?
- Dashed line, shade above
- Dashed line, shade below
- Solid line, shade below
- Solid line, shade above
Boundary rule y = -3x + 4. Rows
x y
0 4
1 1
2 -2
5.
Luz graphs for a science fair. Which drawing shows y ≤ -3x + 4?
- Dashed line, shade below
- Dashed line, shade above
- Solid line, shade above
- Solid line, shade below
Boundary rule y = -x + 4. Rows
x y
0 4
1 3
2 2
6.
Noah graphs on a tablet. Which drawing shows 4 - x ≥ y?
- Dashed line, shade below
- Dashed line, shade above
- Solid line, shade above
- Solid line, shade below
Rule table for y = 3x - 2
x y
0 -2
1 1
2 4
3 7
4 10
7.
Pia plots a point beside a rule. The rule is y = 3x - 2 and the point is (2, 7). Where is the point?
- On the line
- Above the line
- Below the line
Rule table for y = 2x + 1
x y
0 1
1 3
2 5
3 7
4 9
8.
Ren plots a point beside a rule. The rule is y = 2x + 1 and the point is (4, 5). Where is the point?
- Above the line
- On the line
- Below the line
Rule table for y = 4x - 3
x y
0 -3
1 1
2 5
3 9
4 13
9.
Zee plots a point beside a rule. The rule is y = 4x - 3 and the point is (3, 4). Where is the point?
- Above the line
- On the line
- Below the line
Rule table for y = -2x + 10
x y
0 10
1 8
2 6
3 4
4 2
10.
Ari plots a point beside a rule. The rule is y = -2x + 10 and the point is (4, 3). Where is the point?
- Above the line
- Below the line
- On the line

x	y
0	-3
1	-1
2	1
3	3

x	y
0	5
1	4
2	3
3	2

x	y
0	3
1	1
2	-1
3	-3

x	y
0	1
1	3
2	5

x	y
0	4
1	1
2	-2

x	y
0	4
1	3
2	2

x	y
0	-2
1	1
2	4
3	7
4	10

x	y
0	1
1	3
2	5
3	7
4	9

x	y
0	-3
1	1
2	5
3	9
4	13

x	y
0	10
1	8
2	6
3	4
4	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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9th grade Graph and write a two-variable inequality worksheet

Rule table for the boundary y = 2x - 3

Rule table for the boundary y = -x + 5

Rule table for the boundary y = -2x + 3

Boundary rule y = 2x + 1. Rows

Boundary rule y = -3x + 4. Rows

Boundary rule y = -x + 4. Rows

Rule table for y = 3x - 2

Rule table for y = 2x + 1

Rule table for y = 4x - 3

Rule table for y = -2x + 10