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Objective - To write and to graph linear equations that describe dependent relationships. Let n = # of triangles. Independent. Dependent. p. n. Let p = the perimeter of each figure . 1. 3. A) Find an equation that describes p in terms of n. 2. 4. p = n + 2. 3. 5.

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objective to write and to graph linear equations that describe dependent relationships
Objective - To write and to graph linear equations that describe dependent relationships

Let n =# of triangles

Independent

Dependent

p

n

Let p = the perimeter of each figure

1

3

A) Find an equation that describes p

in terms of n.

2

4

p = n + 2

3

5

B) Find the perimeter of 100 such

triangles.

4

6

p = n + 2

5

7

p = 100 + 2

6

8

p = 102

slide2

Let n =# of squares

Let p = perimeter of figure

Independent

Dependent

p

n

1

4

A) Find an equation that describes p

in terms of n.

2

6

p = 2n + 2

3

8

B) Find the perimeter of 405 such

squares.

4

10

p = 2n + 2

5

12

p = 2(405) + 2

6

14

p = 812

slide3

Let n =# of hexagons

Independent

Dependent

Let p = perimeter of figure

p

n

1

6

A) Find an equation that describes p

in terms of n.

4

2

10

4

p = 4n + 2

3

14

4

B) Find the perimeter of 322 such

hexagons.

4

18

4

p = 4n + 2

5

22

4

p = 4(322) + 2

6

26

p = 1290

slide4

Let n =# of triangles

Independent

Dependent

p

n

Let p = the perimeter of each figure

1

3

A) Find an equation that describes p

in terms of n.

2

4

p = n + 2

3

5

B) Find the perimeter of 100 such

triangles.

4

6

p = n + 2

5

7

p = 100 + 2

6

8

p = 102

slide5

Let n =# of squares

Let p = perimeter of figure

Independent

Dependent

p

n

1

4

A) Find an equation that describes p

in terms of n.

2

6

p = 2n + 2

3

8

B) Find the perimeter of 405 such

squares.

4

10

p = 2n + 2

5

12

p = 2(405) + 2

6

14

p = 812

slide6

Instance: 1 2 3 4

# of

Squares: 5 9 13 17

Let n = Instance or Design #

S

n

Let S = Number of Squares Used

1 5

2 9

3 13

4 17

5 21

4

Write an equation that describes

S in terms of n.

4

4

S = ___n + ___

4

1

4

Change

Start Value

slide7

This chart shows the price

of sliced fruit platters.

1) How much would a

6 lb. platter cost?

$8.10 + 1.50 = $ 9.60

1.50

1.50

2) Write an equation for

the cost of a platter that

weighs w lbs.

1.50

1.50

Let p = price of platter

3) How much would a 10 lb.

platter cost?

p = 1.50 w +

0.60

p = 1.50 w + 0.60

Change

Start

Value

p = 1.50 ( 10 ) + 0.60

p = 15.00 + 0.60 = $15.60

slide8

Complete the x-y chart and use it to write a linear

equation for y in terms of x.

x

x

y

y

1)

2)

0

1

2

3

4

5

2

5

8

__

__

__

0

1

2

3

4

5

7

3

-1

__

__

__

3

-4

3

-4

3

-4

11

-5

3

-4

14

-9

3

-4

17

-13

3

2

-4

7

y = ___x + ___

y = ___x + ___

Change

Change

Start

Value

Start

Value

slide9

Complete the x-y chart and use it to write a linear

equation for y in terms of x.

x

x

y

y

3)

4)

-3

-2

-1

0

1

2

5

7

9

__

__

__

-14

-11

-8

__

__

__

-3

-2

-1

0

1

2

2

3

2

3

2

3

11

-5

2

3

13

-2

2

3

15

1

2

11

3

-5

y = ___x + ___

y = ___x + ___

Change

Change

Start

Value

Start

Value

slide10

A taxi cab charges a flat rate of $2.50 and 15 c

per mile. Write a linear equation for the charge

in terms of the number of miles driven.

Let C = charge in dollars

Let m =# of miles driven

C = 2.50 + 0.15 m

Start

Value

Change

slide11

A phone company charges $17.50 per month and 12 c for each additional minute . Write a linear equation for the charge in terms of the number of minutes.

Let C = charge in dollars

Let m =# of minutes

C = 17.50 + 0.12 m

Start

Value

Change

slide12

Jason has $60 and is spending $11 a day.

a) Define variables. Which is dependent?

b) Write an equation to describe the money

Jason has in terms of the days.

c) Make an x-y chart and graph.

slide13

Jason has $60 and is spending $11 a day.

b) y = 60 - 11x

a) Let x =# of days

Let y = Jason’s money

y depends on x

Line is decreasing

60

50

40

30

20

10

c)

x

y

Line is discrete

0

1

2

3

4

5

60

49

38

27

16

5

Jason’s Money ($)

0 1 2 3 4 5 6

# Days

slide14

A car’s fuel tank is filled at a rate of 1.6 gal/min.

The tank held 5 gallons of gas before refueling.

a) Define variables. Which is dependent?

b) Write an equation to describe the volume

of gas in the tank in terms of time.

c) Make an x-y chart and graph.

slide15

A car’s fuel tank is filled at a rate of 1.6 gal/min.

The tank held 5 gallons of gas before refueling.

a) Let m =# of minutes

Let V = Volume of gas in tank

V depends on m

b) V = 5 + 1.6m

c)

30

25

20

15

10

5

m

V

Line is increasing

0

2

4

6

8

10

5

8.2

11.4

14.6

17.8

21

Volume

of gas

in tank

Line is continuous

0 2 4 6 8 10 12

# minutes