Exploring Rates Using a Three-Column Process

Chart (Module 6)

Guided PracticeSituational Rate of Change

Guided PracticeThe Yellow Submarine

Situational Rates of Change (Guided Practice)

For each of the following situations:

1) Complete the depends on sentence,

2) Complete a three column process chart and,

3) Write an equation that models the situation.

1 John went fishing and caught 2 fish in one hour. In two hours he caught 4 fish.

depends onNumber of fish caught number of hours.

Equation_____________y = 2x

1

4

Number of fish caught number of hours

one

2 two

221

22

1

ym

x

222

1 ( )12 ( )

xyy xx

( )

2 Anica is learning to crawl. She was 3 feet away from the door at five seconds. She was 6 feet away at 10 seconds.

Equation_____________

depends onAnica’s distance from door in feet the number of seconds

number of seconds

distance from door in feet

5

10

3

6

3

5y x

3

5( )x

3

5(5)

3

5(10)

353

5

ym

x

A left Hawaii at a constant speed.

After two hours, the submarine is 50

meters below sea level. After 5 hours, the

is 125 meters below sea

level. How fast is the submarine

traveling?

The Yellow Submarine(Guided Practice)

X

y

1 2 3 4 5

–50

–125

Number of Hours

Dis

tanc

e T

rave

led

Bel

ow S

ea L

evel

50

Distance traveled below sea level number of hours

A left Hawaii at a constant speed. After two hours, the

submarine is 50 meters below sea level. After 5 hours, the

is 125 meters below sea level. How fast is the

submarine traveling?

two

depends onDependent Independent

number of hoursDistance traveled below sea level

50

2

5

125

–50

–125–753

y

x

–753 – 25= – 25 – 25

( )2

( )5 – 25 ( )

xyx

x1 2 3 4 5

–50

–125

Number of HoursD

ista

nce

Bel

ow

Se

a L

eve

l (m

)#

hours

Distance below

sea level

5

- 50

- 125

2 - 50

- 125

- 25

- 50

- 75

∆X = 3

∆Y = - 75- 75

2

5

1 2 3

3

Δy= -25

ΔXSlope of the line.

Slope of –25 means …

the submarine goes DOWN under the sea at 25 meters per hour.

y

–25

–75

–100

Find the slope of the line given the points (–5, 2) and (10, –4).

(–5, 2)

(10, – 4)

–66 units down

15 units to the right15

∆y

∆x=

–6

15

÷ 3

÷ 3=

–2

5

1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

-1-2-3-4-5-6-7-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

-8-9-10

8

910

Slope = 2

5

Find the rate of change and equation of the given values in the table shown.

–3

–6

5

10

Equation

x y

–3

∆y∆x

= 5–3

=Rate of Change

5–3

53

– 53

– 53

– 53

–

y = x53

–

–3 ( )

–6 ( )

x ( )

The End