Direct Variation 2

Direct Variation

Another way of describing a relationship between X and Y that is proportional

Use the formula: y = kx

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​Finding x when you know k and y

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Multiple Choice

Eduardo counted ten seconds between seeing lightning and hearing thunder, and he knew that the lightning was about 2 miles away. What is the constant of variation?

• k = 10
• k = 2
• k = 5
• k = 1/5

Multiple Choice

At top speed, a rabbit can cover 7 miles in 12 minutes. What is the constant of variation?

• k = 7
• k = 12
• k = 12/7
• k = 7/12

Multiple Choice

A dishwasher uses 65 gallons of water to wash 5 loads of dishes. What is the constant of variation?

• k = 13
• k = 65
• k = 5
• k = 1/13

Multiple Choice

Suppose y varies directly as x. If x = 15 when y = 12, find x when y = 21.

• 8.57

• 16.8

• 24

• 26.25

Multiple Choice

Suppose y varies directly as x. If x = 27 when y = 6, find x when y = 2.

• 0.44

• 81

• 23

• 9

Multiple Choice

The amount a store earns varies directly as the number of hours. A local store takes in $11,500 in a 4 hour period. Estimate how many hours it would take the store to earn $23,000

• 2 hours

• 8 hours

• 11,504 hours

• 66,125,000 hours

Multiple Choice

The number of apples sold varies directly as the cost. If 4 apples cost $0.45, find the cost of 12 apples.

• $1.35

• $106.67

• $0.45

• $0.15

Multiple Choice

Suppose y varies directly as x. If y = 30 when x = 8, find y when x = 4.

• 1.07

• 15

• 26

• 60

Multiple Choice

Suppose y varies directly as x. If y = 150 when x = 3, find y when x = 5.

• 0.1

• 90

• 153

• 250

Multiple Choice

On a scale, yards vary directly as feet. If 3 feet represent 30 yards, how many yards represent 5 feet.

• 0.5 yards

• 18 yards

• 32 yards

• 50 yards

Multiple Choice

Suppose y varies directly as x. If y = -4 when x = 32, find x when y = -0.375.

• 0.05

• 3

• 27.6

• 341.3

Multiple Choice

The number of books sold varies directly as the cost of the books. If 8 books cost $10.40, how many books can be bought for $32.50?

• 25 books

• 30 books

• 32 books

• 42 books

Multiple Choice

Suppose y varies directly as x. If y = -7 when x = -14, find x when y = 10.

• -5

• 3

• 9.8

• 20

Multiple Choice

Suppose y varies directly as x. If y = 3 when x = 15, find x when y = 5.

• 25

• 17

• 9

• 1

Fill in the Blanks

Y varies directly as X; and Y = 21 when X = 3. Then find X when Y = 42.

Fill in the Blanks

Y varies directly as X, and Y = 8 when X = 16. Then find X when Y = 16.

Fill in the Blanks

Heather’s weekly pay varies directly to the number of hours she works at the record store. Her pay is $174 for 24 hours of work. Find the amount of pay for 40 hours of work.

Multiple Select

Does the table illustrate a direct variation?

• No

• Yes

Multiple Choice

y varies directly with x. If the constant of proportionality is 3 and y = 15, what is x?

• 3

• 15

• 5

• 1/5

Multiple Choice

y varies directly with x. If the constant of proportionality is 6 and y = 24, what is x?

• 6

• 24

• 4

• 1/4

Multiple Choice

y varies directly with x. If the constant of proportionality is 20 and y = 4, what is x?

• 20

• 4

• 5

• 1/5

Multiple Choice

y varies directly with x. If the constant of proportionality is 8 and y = 56, what is x?

• 8

• 56

• 7

• 1/7

Multiple Choice

y varies directly with x. If the constant of proportionality is 5 and y = 5, what is x?

• 5

• 1

• 0

use the formula: k = y/x

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​To find the Constant of Proportionality:

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Multiple Choice

y varies directly with x. If y = 10 and x = 2, what is the constant of proportionality?

• 10

• 2

• 5

• 1/5

Multiple Choice

y varies directly with x. If y = 20 and x = 5, what is the constant of proportionality?

• 20

• 5

• 4

• 1/4

Multiple Choice

y varies directly with x. If y = 50 and x = 5, what is the constant of proportionality?

• 50

• 5

• 10

• 1/10

Multiple Choice

y varies directly with x. If y = 18 and x = 3, what is the constant of proportionality?

• 18

• 3

• 6

• 1/6

Multiple Choice

y varies directly with x. If y = 12 and x = 15, what is the constant of proportionality?

• 12

• 15

• 4/5

• 5/4

In direct variation, one variable will always be a constant multiple of the other.

Constant of Proportionality:

Situations that vary directly can always be represented with the equation

y = K x ( K is your CoP)

K = y/x

To find K you must divide Y by X

Open Ended

If x = 9 and y = 6 then.... k = ______________

What would your equation be? y= _______________

If x = 2 and y =15 then... k = ____________

What would your equation be? y= ____________

Multiple Choice

A person’s weekly pay is directly proportional to the number of hours worked. Shawn’s pay is $123.00 for 20 hours of work. What is the constant of variation?

• k = 123
• k = 20
• k = 6.15
• k = 0.16

Fill in the Blanks

If x is -3 and y is 18, then k =

Fill in the Blanks

If x = 1/4 and y = 7, then what is K?

Fill in the Blanks

If x = 2/3 and y = 24, then what is K?

Now answer the following questions on your own.

Multiple Choice

Determine if the relationship between the two quantities is a direct variation. Explain your reasoning.

• yes, the constant of variation is 1/2

• yes, the constant of variation is 2

• no, there is constant of variation.

Multiple Choice

Determine if the relationship between the two quantities is a direct variation. Explain your reasoning.

• yes, the constant of variation is 2

• yes, the constant of variation is 1/2

• no, there is no constant of variation

Multiple Choice

What does the Direct Variation Equation look like?

• Y= kx
• y = mx + b
• y = b
• y = x

Multiple Choice

Does the equation shown below represent a direct variation?

y=2x

• yes

• no

Multiple Choice

Which of the given graphs is a direct variation?

• A
• B
• C
• D

Multiple Choice

Which graph shows a direct variation?

• A

• B

• C

• D

Multiple Choice

Write the equation for the direct variation, given the table.

• y = 1/3x

• y = 3x

• y = 1/2x

Multiple Choice

Write an equation for this direct variation.

• y=4x

• y=1/8x

• y=1/4x

• y=8x

Multiple Choice

 y varies directly with x, and y is 16 when x is 32. Which equation represents this situation?

• y=32x
• y=16x
• y=2x
• y=(1/2)x

Multiple Choice

In a direct variation, y=39 when x=3.  Find the value of y when x=2.

• 26
• 3
• 58.5
• 2

Multiple Choice

If x = 10.5 and y = 21, what is the equation that represents the direct variation?

• y = -2x

• y = 2x

• y = .5x

• y = 1.5x

• y = 2/3x

Multiple Choice

If x= 20/3 and y = 10, what is the equation that represents the direct variation?

• y = -2x

• y = 2x

• y = .5x

• y = 1.5x

• y=2/3x