Special Linear Relationships

Question 1

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

Revolt · Accepted Answer

k =

Question 2

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?

Revolt · Accepted Answer

F = 32.2m

Question 3

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?

Revolt · Accepted Answer

f(n) = 0.15n + 0.35

Question 4

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

Revolt · Accepted Answer

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

Question 5

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

Revolt · Accepted Answer

y = 7x

Question 6

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

Revolt · Accepted Answer

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).

Question 7

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

Revolt · Accepted Answer

y = x

Question 8

Which graph represents a function with direct variation?

Revolt · Accepted Answer

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

Question 9

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?

Revolt · Accepted Answer

The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.

Question 10

Three points of a function are graphed.

Revolt · Accepted Answer

The function is linear but is not a direct variation function.

Special Linear Relationships Answers

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