Section 2-2Inverse Variation

Warm-upy varies directly as the square of x. If y = 63 when x = 3,

a. Find y when x = 9

Warm-upy varies directly as the square of x. If y = 63 when x = 3,

a. Find y when x = 9

y = kx2

Warm-upy varies directly as the square of x. If y = 63 when x = 3,

a. Find y when x = 9

y = kx2 63 = k(3)2

Warm-upy varies directly as the square of x. If y = 63 when x = 3,

a. Find y when x = 9

y = kx2 63 = k(3)2 63 = 9k

Warm-upy varies directly as the square of x. If y = 63 when x = 3,

a. Find y when x = 9

y = kx2 63 = k(3)2 63 = 9k k = 7

Warm-upy varies directly as the square of x. If y = 63 when x = 3,

a. Find y when x = 9

y = kx2 63 = k(3)2 63 = 9k k = 7

y = 7x2

Warm-upy varies directly as the square of x. If y = 63 when x = 3,

a. Find y when x = 9

y = kx2 63 = k(3)2 63 = 9k k = 7

y = 7x2 y = 7(9)2

Warm-upy varies directly as the square of x. If y = 63 when x = 3,

a. Find y when x = 9

y = kx2 63 = k(3)2 63 = 9k k = 7

y = 7x2 y = 7(9)2 = 7(81)

Warm-upy varies directly as the square of x. If y = 63 when x = 3,

a. Find y when x = 9

y = kx2 63 = k(3)2 63 = 9k k = 7

y = 7x2 y = 7(9)2 = 7(81) = 567

Warm-upy varies directly as the square of x. If y = 63 when x = 3,

a. Find y when x = 9

y = kx2 63 = k(3)2 63 = 9k k = 7

y = 7x2 y = 7(9)2 = 7(81) = 567

b. Find y when x = 5

Warm-upy varies directly as the square of x. If y = 63 when x = 3,

a. Find y when x = 9

y = kx2 63 = k(3)2 63 = 9k k = 7

y = 7x2 y = 7(9)2 = 7(81) = 567

b. Find y when x = 5

y = 7x2

Warm-upy varies directly as the square of x. If y = 63 when x = 3,

a. Find y when x = 9

y = kx2 63 = k(3)2 63 = 9k k = 7

y = 7x2 y = 7(9)2 = 7(81) = 567

b. Find y when x = 5

y = 7x2 y = 7(5)2

Warm-upy varies directly as the square of x. If y = 63 when x = 3,

a. Find y when x = 9

y = kx2 63 = k(3)2 63 = 9k k = 7

y = 7x2 y = 7(9)2 = 7(81) = 567

b. Find y when x = 5

y = 7x2 y = 7(5)2 = 7(25)

Warm-upy varies directly as the square of x. If y = 63 when x = 3,

a. Find y when x = 9

y = kx2 63 = k(3)2 63 = 9k k = 7

y = 7x2 y = 7(9)2 = 7(81) = 567

b. Find y when x = 5

y = 7x2 y = 7(5)2 = 7(25) = 175

Review: Direct Variation

Review: Direct Variation

Wording for Direct Variation

Review: Direct Variation

Wording for Direct Variation

General Equation

Review: Direct Variation

Wording for Direct Variation

General Equation

Constant of Variation

Review: Direct Variation

Wording for Direct Variation

General Equation

Constant of Variation

Steps to solve

“t Varies Inversely as s”:

“t Varies Inversely as s”: When t goes up, s goes down; when t goes down, s goes up

“t Varies Inversely as s”: When t goes up, s goes down; when t goes down, s goes up

Inverse Variation Function:

“t Varies Inversely as s”: When t goes up, s goes down; when t goes down, s goes up

Inverse Variation Function:

A function of the form with k ≠ 0 and n > 0 y =

k

xn

“t Varies Inversely as s”: When t goes up, s goes down; when t goes down, s goes up

Inverse Variation Function:

A function of the form with k ≠ 0 and n > 0 y =

k

xn

“t Varies Inversely as s”: When t goes up, s goes down; when t goes down, s goes up

Inverse Variation Function:

A function of the form with k ≠ 0 and n > 0 y =

k

xn

“ is inversely proportional to”

“t Varies Inversely as s”: When t goes up, s goes down; when t goes down, s goes up

Inverse Variation Function:

A function of the form with k ≠ 0 and n > 0 y =

k

xn

“ is inversely proportional to”

***The intensity of the light varies inversely as the square of the distance from the light source

Example 1Rewrite the statement, “The intensity of the light

varies inversely as the square of the distance from the light source.”

Example 1Rewrite the statement, “The intensity of the light

varies inversely as the square of the distance from the light source.”

The intensity of the light is inversely proportional to the square of the distance from the light source

Example 2In a room, the floor space F per person varies inversely

as the square of the number of people P in the room. Write an equation to represent this situation.

Example 2In a room, the floor space F per person varies inversely

as the square of the number of people P in the room. Write an equation to represent this situation.

F =

k

p2

Example 3The time T required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement

workers to do a job. How long would it take 12 workers to do the same job?

Example 3The time T required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement

workers to do a job. How long would it take 12 workers to do the same job?

T =

k

w

Example 3The time T required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement

workers to do a job. How long would it take 12 workers to do the same job?

T =

k

w 5 =

k

8

Example 3The time T required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement

workers to do a job. How long would it take 12 workers to do the same job?

T =

k

w 5 =

k

8k = 40

Example 3The time T required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement

workers to do a job. How long would it take 12 workers to do the same job?

T =

k

w 5 =

k

8k = 40

T =

40

w

Example 3The time T required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement

workers to do a job. How long would it take 12 workers to do the same job?

T =

k

w 5 =

k

8k = 40

T =

40

w

T =

40

12

Example 3The time T required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement

workers to do a job. How long would it take 12 workers to do the same job?

T =

k

w 5 =

k

8k = 40

T =

40

w

T =

40

12 = 3 13 hours

Steps to solving an inverse variation problem

Steps to solving an inverse variation problem

1. Write an equation to describe the variation

Steps to solving an inverse variation problem

1. Write an equation to describe the variation

2. Find k

Steps to solving an inverse variation problem

1. Write an equation to describe the variation

2. Find k

3. Rewrite the function using k

Steps to solving an inverse variation problem

1. Write an equation to describe the variation

2. Find k

3. Rewrite the function using k

4. Evaluate

Example 4g is inversely proportional to h. If g = 3 when h = 6,

find g when h = 9.

Example 4g is inversely proportional to h. If g = 3 when h = 6,

find g when h = 9.

g =

k

h

Example 4g is inversely proportional to h. If g = 3 when h = 6,

find g when h = 9.

g =

k

h 3 =

k

6

Example 4g is inversely proportional to h. If g = 3 when h = 6,

find g when h = 9.

g =

k

h 3 =

k

6k = 18

Example 4g is inversely proportional to h. If g = 3 when h = 6,

find g when h = 9.

g =

k

h 3 =

k

6k = 18

g =

18

h

Example 4g is inversely proportional to h. If g = 3 when h = 6,

find g when h = 9.

g =

k

h 3 =

k

6k = 18

g =

18

h

g =

18

9

Example 4g is inversely proportional to h. If g = 3 when h = 6,

find g when h = 9.

g =

k

h 3 =

k

6k = 18

g =

18

h

g =

18

9= 2

Homework

Homework

p. 81 #1 - 23