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Special Linear Relationships Answers

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Three points of a function are graphed.

Question illustration
A
The function is a direct variation function with a constant of variation of 1.5.
B
The function is a direct variation function with a constant of variation of 1.8.
C
The function is linear but is not a direct variation function.
D
The function is not a linear function.
2
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The graph represents the direct variation function between earnings in dollars and hours worked.

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A
E = 1.5h
B
E = 7.5h
C
E = 13h
D
E = 15h
3

The pattern of numbers below is an arithmetic sequence:14, 24, 34, 44, 54, ...Which statement describes the recursive function used to generate the sequence?

A
The common difference is 1, so the function is f(n + 1) = f(n) + 1 where f(1) = 14.
B
The common difference is 4, so the function is f(n + 1) = f(n) + 4 where f(1) = 10.
C
The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.
D
The common difference is 14, so the function is f(n + 1) = f(n) + 14 where f(1) = 10.
4

Which graph represents a function with direct variation?

A
A coordinate plane with a U shaped line graphed with the minimum at (0, 0).
Option A
B
A coordinate plane with a V shaped line graphed with the minimum at (0, 0).
Option B
C
A coordinate plane with a line passing through (negative 4, 2), (0, 0) and (4, negative 2).
Option C
D
A coordinate plane with a line passing through (negative 2, negative 3), (0, 1) and (1, 3).
Option D
5

The points (3, 24) and (7, 56) represent points of a function where y, the number of photographs, varies directly with x, the number of pages in an album. Which statement describes another point on the graph of this function?

A
A 50-page photo album holds 400 photographs.
B
An 80-page photo album holds 560 photographs.
C
A 100-page photo album holds 8,000 photographs.
D
A 900-page photo album holds 8,400 photographs.
6

A direct variation function contains the points (–8, –6) and (12, 9). Which equation represents the function?

A
y = –x
Option A
B
y = –x
Option B
C
y = x
Option C
D
y = x
Option D
7

The table represents a bicycle rental cost in dollars as a function of time in hours.

Question illustration
A
This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
B
This function represents a direct variation because it has a positive, constant rate of change of $10 per hour.
C
This function does not represent a direct variation because it does not represent the cost for 1 hour.
D
This function does not represent a direct variation because the function rule for the cost is to add $10, not multiply by a constant.
8

A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?

A
y =
Option A
B
y =
Option B
C
y = 7x
D
y = 14x
9

What is the constant of variation, k, of the direct variation, y = kx, through (–3, 2)?

A
k = –
Option A
B
k = –
Option B
C
k =
Option C
D
k =
Option D
10

What is the constant of variation, k, of the direct variation, y = kx, through (5, 8)?

A
k = –
Option A
B
k = –
Option B
C
k =
Option C
D
k =
Option D

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