Variation

Variation

Objectives: - Write equations for direct, inverse, and joint variations. - Use variation equations to make predictions.

Cost (Tenths of Dollars)

Number of Cookies

Constant of variation is given by k.k describes how variables relate.

Constant of Variation

Constant of variation is given by k.k describes how variables relate.

Constant of Variation

For example: 5 candy bars cost $10. 3 candy bars cost $6. k = $2 for each candy bar. You can write this relationship as y = 2x where y is the cost of x number of candy bars.

Example: The temperature in an oven varies directly with how long it's been warming up. After 5 minutes, the temperature in the oven was 60 degrees. Find k.

Has the form y = kx

Direct Variation

In the previous example, the total cost varies directly with the number of candy bars. y increases by 2 as x increases by 1. y = 2x

Has the form y = kx

Direct Variation

Y varies directly with x. If y = -88 when x = 11, what is y when x = 50?

y varies directly with x.y is 5 when x is 15. What is the constant of variation? a. 3 b. 1/3 c. 75

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If y varies directly with x and the constant of variation is 8, what equation represents the relationship between x and y?a. y = 8xb. y = 1/8xc. x = 8y

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y varies indirectly with x

inverse variation

For example It takes 2 men 6 days to paint a barn, but it takes 3 men 4 days. So k = 12. The relationship is given by In how many days would 5 men paint the fence?

y varies indirectly with x

inverse variation

y varies inversely with x. When x is 3, y is 2.What is the constant of variation?

y varies indirectly with x

inverse variation

If y varies inversely with x, and the constant of variation is 11, what is the equation that describes this relationship?

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Brain Break!

y varies inversely with x

inverse variation

y varies directly with x y = kx

Direct variation

z varies directly with x and inversely with y

combined variation

z varies directly with x and y z = kxy

joint variation

Example z varies directly with x and inversely with y. When x = 4 and y = 5, z = 8. What is the value of z when x = 8 and y = 10?

variation problems

A question will typically name two or three variables and how they relate. Your job is to find k, and write a general equation that can be used to find all values in that relation.

Step 1

Step 2

Step 3

Step 4

Use your general equation to find a value the question asks.

Substitute the given values for each variable and solve for k.

Decide which formyou are using based on the info in the question.

Write a general equation, only replacing k with the value you found.

Example z varies jointly with x and y. When x = 12 and y = 10, z = 6. What is the value of z when x = 5 and y = 7?

variation problems

A question will typically name two or three variables and how they relate. Your job is to find k, and write a general equation that can be used to find all values in that relation.

Step 1

Step 2

Step 3

Step 4

Use your general equation to find a value the question asks.

Substitute the given values for each variable and solve for k.

Decide which formyou are using based on the info in the question.

Write a general equation, only replacing k with the value you found.

y varies directly with x. When x = 12.5 and y = 25, what is the value of y when x = 50? a. 2 b. 25 c. 100

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Variation

You should be able to: - Write equations for direct, inverse, and joint variations. - Use variation equations to make predictions.