Special Linear Relationships: Assignment

What other points are on the line of direct variation through (5, 12)? Check all that apply.

1. (0, 0) 2. (2.5, 6) 4. (7.5, 18) 6. (15, 36)

Consider the sequence of numbers: 3/8, 3/4, 1 1/8, 1 1/2, 1 7/8, . . .

B. The sequence is recursive and can be represented by the function f(n + 1) = f(n) + 3/8

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

Graph Two

Organic foods in local stores are typically more expensive than conventional foods. The table below compares recent organic and conventional prices per pound for carrots and apples. Use the table to answer the questions. Do the organic prices vary directly with the conventional prices? If so, identify k. Does the total cost of organic apples vary directly with the number of pounds of organic apples purchased? If so, identify k.

1. No, this is not a direct variation. 2. Yes, this is direct variation with k=2.34

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. What is the constant of variation? What is the equation representing the direct variation?

1. 1/9 2. y=(1/9)x

Use the information in the article and associated document about organic strawberry farming to answer the questions about sales appropriation. The document is located at this article. Use the data table towards the end of the article to answer the questions. The total operating cost to run the organic strawberry farm varies directly with its number of acres. What is the constant of variation in this scenario? If the total operating cost for a 20-acre organic strawberry farm is $551,520, how many acres are on a farm with a total operating cost of $441,216?

1. 27, 576 2. 16 acres

The first five terms of an arithmetic sequence are shown below: 20, 17, 14, 11, 8, . . . Let n represent the term number and f(n) the term in the sequence. The function _______ represents the sequence.

f(n)=-3n+23

Economists study the way society uses its resources. One important resource studied is agriculture. The recent increase in demand for organic produce has created some interesting economic scenarios for both farmers and consumers. Click the article to learn key facts about the economics of organic produce and answer a few questions. Which is a reason that organic farming is more expensive than conventional farming? How many years must a farm be run organically before its produce can be labeled as "organic"? What is a benefit of crop rotation?

1. Organic farmers must pay for a costly certification process. 2. 3 3. Rotating crops can help build healthy soil.

There are so many little things that go into organic farming and each of them adds additional costs. Some of these additional costs are listed in the article located here. Use the data table at the end of the document to answer the questions. Which cost category in the table shows an example of direct variation? The total cost for office expenses to run the organic strawberry farm varies directly with the number of months it is used. Which equation represents this scenario? What would be the total cost for office expenses for 24 months?

1. Weed-hand 2. y=63x 3. $1,512.00

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?

A. Yes, y=2x

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

A. f(n) = 0.6n + 1.9

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. Figure 1: 9 cubes Figure 2: 13 cubes Figure 3: Figure 4: Figure 5:

Blank One: 17 cubes Blank Two: 21 cubes Blank Three: 25 cubes

A 3-pound bag of apples costs $5.25. What is the unit price of a pound of apples? ____ per pound At this rate, how many pounds of apples can be purchased for $17.50? _____ pounds of apples Let x represent the number of pounds of apples and y the total cost of the apples. What is the equation that represents the direct variation between the total cost of the apples and the number of pounds of apples?

Blank One:$1.75 Blank Two: 10 Blank Three: y=1.75x

Based on what you learned about the economics of organic produce, explain why buying organic food is so expensive and how that relates to direct variation.

Sample Answer: Since there are greater costs to farming organically, organic produce is more expensive for consumers. The total cost to produce an organic crop relates directly to the price consumers pay for it.

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.

Sample Answer: No, the triangular numbers are not a direct variation. There is not a constant of variation between a number and its position in the sequence. The ratios of the numbers to their positions are not equal. Also, the points (1, 1), (2, 3), (3, 6), and so on, do not lie on a line.