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Direct Variation. Objective: to solve for k and set up a direct variation equation. Direct Variation. Constant : A value that does not change Example: 1.6 km per mile Directly proportional : two variables that have a constant ratio. Example: Direct variation : An equation in the form

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direct variation

Direct Variation

Objective: to solve for k and set up a direct variation equation

direct variation1
Direct Variation

Constant: A value that does not change

Example: 1.6 km per mile

Directly proportional: two variables that have a constant ratio.

Example:

Direct variation: An equation in the form

y = kx,

kis the constant of variation and can be found when you take y and divide it by x.

Example: y = 1.6x, where y is kilometers andx is miles.

slide3

The cost of a soft drink varies directly with the number of ounces you buy. It costs $.96 for a 12 oz. bottle.

The steps to follow to write a direct variation equation:

1. What is the generic formula for a direct variation equation?

y = kx

2. What is the variation constant (k) for this problem?

k = 0.08

3. What is the equation for this problem? (make it specific for this problem)

c = kn, where c = cost and n = ounces

c = .08n

4. How much does it cost to buy a 16 oz pop bottle?

c = .08(16)

c = $1.28

c = .08n

slide4

The cost of gasoline varies directly with the number of gallons bought. It costs $33 to buy 12 gallons of gas.

The steps to follow to write a direct variation equation:

1. What is the generic formula for a direct variation equation?

y = kx or k = y/x

2. What is the variation constant (k) for this problem?

k = 2.75

3. What is the equation for this problem? (make it specific for this problem)

c = 2.75n

c = kn, where c = cost and n= gallons bought

4. How much does it cost to buy 7.5 gallons of gas?

c = 2.75(7.5)

c = $20.63

c = 2.75n

slide5

A worker earns $1010 in a 40 hour work week.

The steps to follow to write a direct variation equation:

Hours

$

1. What is the generic formula for a direct variation equation?

$___

hours

y = kx

2. What is the variation constant (k) for this problem?

k = 25.25

3. What is the equation for this problem? (make it specific for this problem)

m = 25.25h

m = kh, where m = money earned and h = hours worked

4. How many hours did he work if he got paid $4848.

4848 = 25.25 (h)

h = 192

m = 25.25h

assignment
assignment
  • Direct variation worksheet 1-5