Special Linear Relationships Answers

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

The conversion of square feet to square yards can be represented by direct variation. Three square yards are equivalent to 27 square feet. Let y represent the number of square yards and x the number of square feet. Then y varies directly with x.

✔ y = (1/9)xy = (1/3)xy = 3xy = 9x

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.

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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

✔ 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?

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?

What other points are on the line of direct variation through (5, 12)? Check all that apply.(0, 0)(2.5, 6)(3, 10)(7.5, 18)(12.5, 24)(15, 36)

Consider the sequence of numbers: , , 1 StartFraction 3 Over 8 EndFraction, StartFraction 3 Over 4 EndFraction, 1 and StartFraction 1 Over 8 EndFraction, 1 and StartFraction 1 Over 8 EndFraction, 1 and StartFraction 7 Over 8 EndFraction. . . , 1 , 1, . . . Which statement is a description of the sequence?

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