AnswersAPSB 2025 Math Essentials-ALPGraphing Two-Variable Linear Inequalities

Graphing Two-Variable Linear Inequalities — Unit test Answers

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On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 2, 3) and (0, negative 1). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (1, 0). Everything to the right of the line is shaded.

Question illustration
A
y<−2x+2
B
y>−2x+2
C
y<2x−2
D
y>2x−2
2
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Which ordered pair is in the solution set of the system of linear inequalities?y > x – 1y < x – 1

Question illustration
A
(–5, 2)
B
(2, 2)
C
(5, 2)
D
no solution
3

Which description of the graph of the linear inequality y ≥ 7x – 4 is correct?

A
The graph will be a dashed line with a y-intercept of negative four and a slope of seven. The graph will be shaded below the line.
B
The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.
C
The graph will be a solid line with a y-intercept of seven and a slope of negative four. The graph will be shaded below the line.
D
The graph will be a dashed line with a y-intercept of seven and a slope of negative four. The graph will be shaded above the line.
4

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2), and (1, negative 1). Everything to the right of the line is shaded.

Question illustration
A
(0, 2)
B
(2, 0)
C
(1, −2)
D
(−2, 1)
5

Which inequality is graphed below?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
6

Which graph represents ?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
7

On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 1.3) and (3, negative 0.3). Everything below and to the right of the line is shaded.

Question illustration
A
y ≤ x – 1.3
Option A
B
y ≤ x –
Option B
C
y ≥ x –
Option C
D
y ≥ x – 1.3
Option D
8

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) and (2, 0). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded.

Question illustration
A
y > x – 2 and x – 2y < 4
B
y > x + 2 and x + 2y < 4
C
y > x – 2 and x + 2y < 4
D
y > x – 2 and x + 2y < –4
9

Which ordered pair makes both inequalities true?y –x + 4

Question illustration
A
(4,0)
B
(1,2)
C
(0,4)
D
(2,1)
10

Lionel plays trumpet for a minimum of 45 minutes on the days that he practices. If x is the number of days that Lionel practices and y is the total number of hours he spends practicing, which inequality represents this situation?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
11

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to the left of the line is shaded.

Question illustration
A
y < x + 3
Option A
B
y > x + 3
Option B
C
y > x + 3
Option C
D
y < x + 3
Option D
12

A movie theater is giving away a souvenir poster to any customer with a concession stand receipt that exceeds $60. The theater sells a bag of popcorn for $6 and bottle of soda for $3.50. Let x represent the number of bags of popcorn, and let y represent the number of bottles of soda. Which linear inequality can be used to find the quantities of popcorn and soda that should be purchased to receive a poster?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
13

Which ordered pairs make both inequalities true? Select two options. y x + 1

Question illustration
A
(–1, 3)
B
(0, 2)
C
(1, 2)
D
(2, –1)
E
(2, 2)
14

Which ordered pair makes both inequalities true?y > –3x + 3y > 2x – 2

Question illustration
A
(1,0)
B
(–1,1)
C
(2,2)
D
(0,3)
15

Which notation best represents the phrase “at least 24”?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
16

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything to the right of the line is shaded.

Question illustration
A
y ≤ x + 2
Option A
B
y ≥ x + 2
Option B
C
y ≤ x + 2
Option C
D
y ≥ x + 2
Option D
17

Which is the graph of the linear inequality x – 2y > –6?

Question illustration
A
Option
B
Option
C
Option
D
Option
18

Question text not available

Question illustration
A
y > x – 2 and y < x + 1
B
y x + 1
C
y x + 1
D
y > x – 2 and y < x + 1
19

Which graph shows the solution to the system of linear inequalities?y > x + 3y ≤ x + 2

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
20

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, 3) and (3, 4). Everything above the line is shaded. The second dashed line has a positive slope and goes through (0, negative 2) and (1, 1). Everything to the right of the line is shaded.

Question illustration
A
y > x + 3 and 3x – y > 2
Option A
B
y > x + 3 and 3x – y > 2
Option B
C
y > x + 3 and 3x + y > 2
Option C
D
y > x + 3 and 2x – y > 2
Option D

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