Lesson 6-9: Variation

Objective:Students will:oFind the constant of variation and setup direct and inverse variation equationsoUse variation equations to solve problems

Direct Variation

Equations: or

Why direct?

Take or , where k = 2

If y goes up, x must go up

y and x move the same → direct

“k” is the constant of variation – must stay constant

kx

y kxy

28

16 8216

Inverse Variation

Equations: or

Inverse → opposite → if y goes up, x must go down…

kyx x

ky

Choosing

Identify the variables

Ask: if the one value increases, what will the other do?

increase also → direct

decrease → inverse

Example 1

The force applied to a spring causes the length to increase. 8 pounds makes the spring 4 inches. Find k and write a general equation.

Which type of variation?

Direct

What would be the x variable? y?

x: pounds y: inches

kx

y

k8

4

k2

1

xy2

1

What would be the length if the weight is 20lbs?

iny 10)20(2

1

Example 2

Time (t) required to do a job varies inversely with the number of people working. It takes 4hrs for 12 people to put up bleachers. Write the equation to represent the problem.

How long would it take 3 people to do the same job.

kyx

k 412

k48x

y48

3

48y hrsy 16

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