Answers2025-2026_MDCPS_1205070-MJ Grade 8 Pre-Algebra Sem 1-CRInterpreting Graphs

Constructing Linear Functions Answers

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1
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Is the function represented by the table linear?xy10–61111261312

A
Yes, because it has a constant rate of change.
B
Yes, because it does not have a constant rate of change.
C
No, because it has a constant rate of change.
D
No, because it does not have a constant rate of change.
2
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What is the rate of change of the function?

Question illustration
A
–2
B
Negative one-half
Option B
C
One-half
Option C
D
2
3

Which graph represents a function with a rate of change of 0.5?

A
On a coordinate plane, a line with negative slope goes through points (negative 1, 1) and (0, negative 1).
Option A
B
On a coordinate plane, a line with negative slope goes through points (negative 2, 0) and (0, negative 1).
Option B
C
On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (1, 1).
Option C
D
On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (2, 0).
Option D
4

The table below represents the number of math problems Jana completed as a function of the number of minutes since she began doing her homework. Does this situation represent a linear or non-linear function, and why?Jana’s Math Homework ProgressMinutesMath Problems Completed1327312416519

A
It represents a linear function because there is a constant rate of change.
B
It represents a linear function because there is not a constant rate of change.
C
It represents a non-linear function because there is a constant rate of change.
D
It represents a non-linear function because there is not a constant rate of change.
5

Which of these tables represents a linear function?

A
A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 4, 5, 6. Column 2 is labeled y with entries 3, 4, 6, 7.
Option A
B
A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 4, 5, 6. Column 2 is labeled y with entries 6, 5, 4, 3.
Option B
C
A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 4, 5, 6. Column 2 is labeled y with entries 7, 6, 5, 3.
Option C
D
A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 4, 5, 6. Column 2 is labeled y with entries 2, 4, 5, 6.
Option D
6

Look at the graph of the linear function. The rate of change between point A and point B is 2. What is the rate of change between point C and point D?

Question illustration
A
–2
B
Negative one-half
Option B
C
One-half
Option C
D
2
7

Willis analyzed the following table to determine if the function it represents is linear or non-linear. First he found the differences in the y-values as 7 – 1 = 6, 17 – 7 = 10, and 31 – 17 = 14. Then he concluded that since the differences of 6, 10, and 14 are increasing by 4 each time, the function has a constant rate of change and is linear. What was Willis’s mistake?xy1127317431

A
He found the differences in the y-values as 7 – 1 = 6, 17 – 7 = 10, and 31 – 17 = 14.
B
He determined that the differences of 6, 10, and 14 are increasing by 4 each time.
C
He concluded that the function has a constant rate of change.
D
He reasoned that a function that has a constant rate of change is linear.
8

Which of these tables represents a non-linear function?

A
A 2-column table with 4 rows. Column 1 is labeled x with entries 17, 18, 19, 20. Column 2 is labeled y with entries 20, 19, 18, 17.
Option A
B
A 2-column table with 4 rows. Column 1 is labeled x with entries 17, 18, 19, 20. Column 2 is labeled y with entries negative 16, negative 17, negative 18, negative 19.
Option B
C
A 2-column table with 4 rows. Column 1 is labeled x with entries 17, 18, 19, 20. Column 2 is labeled y with entries 16, 17, 19, 20.
Option C
D
A 2-column table with 4 rows. Column 1 is labeled x with entries 17, 18, 19, 20. Column 2 is labeled y with entries negative 20, negative 19, negative 18, negative 17.
Option D
9

Juno is taking a taxi. The table represents a linear function and shows the amount she owed after various numbers of miles traveled. Is the rate of change 2.25?Amount Juno Owed for a TaxiMilesAmount Owed (dollars)12.524.753749.25511.5

A
Yes, because the amount owed changes by 1 every time the miles change by 2.25.
B
Yes, because the amount owed changes by 2.25 every time the miles change by 1.
C
No, because the amount owed does not change by 1 every time the miles change by 2.25.
D
No, because the amount owed does not change by 2.25 every time the miles change by 1.
10

What is the rate of change of the function represented by the table?xy1–8.52–63–3.54–1

A
–2.5
B
–1
C
1
D
2.5

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