AnswersAPSB 2025 Math Essentials-ALPGraphing Two-Variable Linear Inequalities

Graphing Two-Variable Linear Inequalities — Unit test Answers

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1
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Which description of the graph of the linear inequality y > 3x – 8 is correct?

A
The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded below the line.
B
The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded above the line.
C
The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded below the line.
D
The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line.
2
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Which statements are true about the graph of the system of linear inequalities? Select two options.y > 3x – 4y < x + 1

Question illustration
A
The graph of y > 3x − 4 has shading above a dashed line.
B
The graph of y < x + 1 has shading below a dashed line.
Option B
C
The graphs of the inequalities will intersect.
D
There are no solutions to the system.
E
The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).
3

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

Question illustration
A
y > x + 1
B
y < x – 1
C
y > x – 1
D
y < x + 1
4

An amusement parks sells adult tickets for $18 each and youth tickets for $12 each. Kalila is using the inequality to find the combinations of tickets she can buy without exceeding her $250 budget. The ordered pair (4, 3) is a solution of the inequality. What does (4, 3) represent?

Question illustration
A
Kalila purchases 4 tickets, 3 of which are youth tickets.
B
Kalila purchases 4 tickets, 3 of which are adult tickets.
C
Kalila purchases 4 adult tickets and 3 youth tickets.
D
Kalila purchases 4 youth tickets and 3 adult tickets.
5

Which is true about the solution to the system of inequalities shown?y > 3x + 1y < 3x – 3

Question illustration
A
Only values that satisfy y > 3x + 1 are solutions.
B
Only values that satisfy y < 3x – 3 are solutions.
C
Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.
D
There are no solutions.
6

The sum of two numbers is no more than 28. Let x represent the first number, and let y represent the second number. Which inequality represents this situation?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
7

On a coordinate plane, a dashed straight 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
(2, 3)
B
(2, 1)
C
(3, –2)
D
(–1, 3)
8

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 3) and (3, 1). Everything below and 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 + 1
Option C
D
y < x – 1
Option D
9

In which context will the inequality 4x + 5y > 80 have only integers in its solution set?

A
when x represents prices, in dollars, of adult tickets and y represents prices, in dollars, of student tickets
B
when x represents weights, in pounds, of apples and y represents weights, in pounds, of oranges
C
when x represents time, in hours, spent babysitting and y represents time, in hours, working at a bakery
D
when x represents the number of cats and y represents the number of dogs
10

A local store’s clearance rack is full of DVDs selling for $8 each and CDs selling for $6 each. Let x represent the number of DVDs, and let y represent the number of CDs. Which inequality can be used to find combinations of DVDs and CDs that can be bought with a $50 gift card?

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

Which ordered pairs are in the solution set of the system of linear inequalities?y > x + 2y < 2x + 3

Question illustration
A
(2, 2), (3, 1), (4, 2)
B
(2, 2), (3, –1), (4, 1)
C
(2, 2), (1, –2), (0, 2)
D
(2, 2), (1, 2), (2, 0)
12

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, negative 1). Everything to the left of the line is shaded.

Question illustration
A
y > 2x + 3
B
y < 2x + 3
C
y > −2x + 3
D
y < −2x + 3

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