Answers Algebra IAnalyzing Tables

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

k = –

k = –

k =

k =

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Which graph represents a function with direct variation?

A coordinate plane with a U shaped line graphed with the minimum at (0, 0).

A coordinate plane with a V shaped line graphed with the minimum at (0, 0).

A coordinate plane with a line passing through (negative 4, 2), (0, 0) and (4, negative 2).

A coordinate plane with a line passing through (negative 2, negative 3), (0, 1) and (1, 3).

Which graph represents a function with direct variation?

A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2).

A coordinate plane with a line passing through (negative 5, 4) and (0, 3).

A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3).

A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4).

The sequence below shows Marisa’s library fine starting on the first day her book is overdue and for each additional day afterward:$0.50, $0.65, $0.80, $0.95, $1.10, ...Let f(n) represent Marisa’s library fine (in dollars), where n is the number of days the book has been overdue, starting with n=1 for the first day overdue.Which equation represents Marisa’s library fine as a function of a book that is n days overdue?

f(n) = 0.15n

f(n) = 0.50n

f(n) = 0.15n + 0.35

f(n) = 0.50n + 0.15

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

y = –x

y = x

The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents F, the force on an object due to gravity according to m, the object’s mass?

F = 16.1m

F =

F = 32.2m

F =

A catering company uses different functions to estimate the itemized costs for a party. The table below represents the included tip for wait staff as a function of the number of guests served.

t = 1.8g

t =

g = 1.8t

g =

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

y =

y = 7x

y = 14x

Which graphs show functions with direct variation? Select three options.

A coordinate plane showing Parking Garage Rates with Time in hours on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2.4) and (5, 4).

A coordinate plane showing Cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5).

A coordinate plane showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6).

A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).

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

k = –

k =

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

This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.

This function represents a direct variation because it has a positive, constant rate of change of $10 per hour.

This function does not represent a direct variation because it does not represent the cost for 1 hour.

This function does not represent a direct variation because the function rule for the cost is to add $10, not multiply by a constant.

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 50-page photo album holds 400 photographs.

An 80-page photo album holds 560 photographs.

A 100-page photo album holds 8,000 photographs.

A 900-page photo album holds 8,400 photographs.

Which sequence is generated by the function f(n + 1) = f(n) – 2 for f(1) = 10?

–10, –12, –14, –16, –18, ...

–2, 8, 18, 28, 38, ...

8, 18, 28, 38, 48, ...

10, 8, 6, 4, 2, ...

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