Special Linear Relationships Answers

Figure 3: cubes

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✔ y = (1/9)xy = (1/3)xy = 3xy = 9x

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A 3-pound bag of apples costs $5.25. What is the unit price of a pound of apples?

8 9✔ 10 11

y = 1.25x✔ y = 1.75xy = 2.25xy = 2.75x

A prepaid cell phone charges a preset number of minutes to use text messaging. The graph represents y, the number of minutes used for x, the number of text messages sent and received. Is there a direct variation? Which equation represents the relationship?Yes, y = 2x.Yes, y = 20x.No, y = x + 10.No, y = x + 20.

This sequence represents the diameters of circles used to create an art project:2.5 cm, 3.1 cm, 3.7 cm, 4.3 cmLet f(n) represent diameter in centimeters and n the term number in the sequence. Which equation represents the sequence of diameters?f(n) = 0.6n + 1.9f(n) = 0.6n + 2.5f(n + 1) = f(n) + 1.9f(n + 1) = f(n) – 0.6

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Consider the sequence of numbers: , , 1, 1 , 1, . . . Which statement is a description of the sequence?The sequence is recursive, where each term is greater than its preceding term.The sequence is recursive and can be represented by the function f(n + 1) = f(n) + .The sequence is arithmetic, where each pair of terms has a constant difference of .The sequence is arithmetic and can be represented by the function f(n + 1) = f(n).

Triangular numbers can be represented with equilateral triangles formed by dots. The first five triangular numbers are 1, 3, 6, 10, and 15. Is there a direct variation between a triangular number and its position in the sequence? Explain your reasoning.

Which linear relationship can be described as a function with direct variation?

Which linear relationship can be described as a function with direct variation?

Luis uses cubes to represent each term of a pattern based on a recursive function. The recursive function defined is f(n + 1) = f(n) + 4, where n is an integer and n ≥ 2. The number of cubes used in each of the first two figures is shown below. How many cubes does Luis use in the third, fourth, and fifth figures of the pattern? Fill in the blanks.

✔ f(n) = –3n + 23f(n) = –3n + 61f(n) = 20 – 3nf(n) = 20n – 3

A prepaid cell phone charges a preset number of minutes to use text messaging. The graph represents y, the number of minutes used for x, the number of text messages sent and received. Is there a direct variation? Which equation represents the relationship?