focus 1 and 2 review. evaluating tables for proportional relationships consider the following table:...

Focus 1 and 2 Review

Evaluating tables for proportional relationshipsConsider the following table:

Time in seconds (t)

Distance in meters (d)

0 0

1 2

2 4

3 6

4 8

5 10

Does the table represent a proportional relationship?


Time in seconds (t)


0 0

1 2

2 4

3 6

4 8

5 10


Look for patterns+1

+1

+1

+1+1

+2

+2

+2

+2

+2

x2

x2

x2

x2

x2

x2

Independent variable x-axis

Dependent variable y-axis


Time in seconds (t)


0 0

1 2

2 4

3 6

4 8

5 10

Graph the points

0 1 2 3 4 5 60

2

4

6

8

10

12


Time in seconds (t)

Dis

tanc

e in

met

ers

(d)

What is the equation that matches with this graph?Identify the constant of proportionality and write your equation in the form d=kt


Time in seconds (t)


0 0

1 1.5

2 3

3 4.5

4 6

5 7.5


Is there a pattern?

If you graphed it, does it create a straight line starting at (0,0)?

Can you write an equation that matches this table?

Evaluating tables for proportional relationships

Consider the following table:

Time in seconds (t)


0 0

1 5

2 8

3 12

4 17

5 23



Time in seconds (t)


0 0

1 -3

2 -6

3 -9

4 -12

5 -15


Graphs of proportional relationships

0 1 2 3 4 5 6 70

10

20

30

40

50

60

70

80

90

100

Time

Dis

tanc

e

What is the constant of proportionality?


0 1 2 3 4 5 6 70

5

10

15

20

25

30

Time

Dis

tanc

e



0 1 2 3 4 5 6 70

2

4

6

8

10

12

14

16

Time

Dis

tanc

e


Identifying the constant of proportionality

Anna is walking to school at a constant rate. She writes the equation d=5s to represent the distance (d) in meters she walks in seconds (s). What does the 5 represent in this equation?

Write a verbal model of the equation:

Distance = 5 x seconds

The 5 represents the unit rate of 5 meters/second.


The CMS math department is buying pizza to celebrate students’ success on the end-of-year math test. The equation C=4n represents the total cost (C) for the number of pizzas (n) that they need to get for the celebration. What does the 4 represent? Write a verbal model of the equation:

Total Cost = 4 x number of pizzas

The 4 represents the unit rate of $4/pizza.


Alejandro bought pencils for his math class. The equation C=.18n represents the total cost (C) for the number of pencils (n) that that he bought. What does the .18 represent? Write a verbal model of the equation:

Total Cost = .18 x number of pencils

The .18 represents the unit rate of $.18/pencil.

Writing rates using rational numbersPeter can paint 2/5 of a house in 3/5 of an hour. How much can he paint in one hour?

=

Writing rates using rational numbersA wheel makes 1/8 of a rotation every 2/3 of an hour. How many rotation does the wheel make in 1 hour?

=

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation

The graph below shows how much the soccer team earned washing cars.

0 2 4 6 8 10 120

10

20

30

40

50

60

Number of cars

Amou

nt e

arne

d (m

) What does the point (0,0) mean?

Which point represents the rate in dollars the soccer teams earns per car?

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation

The graph below shows the relationship between distance (d) and gallons (g) of gasoline.

0 10 20 30 40 50 600

200

400

600

800

1000

1200

Gasoline (g)

Dis

tanc

e (d

)

Which point represents the rate in distance traveled for each gallon of gasoline?

What does the point (0,0) mean?

focus 1 and 2 review. evaluating tables for proportional relationships consider the following table:...

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