1. Identifying and Representing Proportional Relationships

2. Discovering Proportional Relationships
A giant tortoise moves at a slow but steady pace. It takes the giant tortoise 3 seconds to travel 10.5 inches.
How far does the tortoise travel in 1 second?
Suppose the tortoise travels 12 seconds. How could you find the distance the tortoise travels?

3. Important Terms
Rate of Change: is a rate that describes how one quantity changes in relation to another quantity.
Proportional Relationship: a relationship in which the rate of change is constant.

4. Important Terms
Proportion: a statement that two rates or ratios are equivalent.
Constant of Proportionality (k): The ratio of the two quantities or y=kx
Must be multiplied by a constant amount to get your output.

5. Finding the Constant of Proportionality
To find k you must divide the y value by the x value.

6. Finding the Constant of Proportionality Ex. 1
Determine the constant of proportionality.
Hours Worked (x) 1 2 3 4
Total Earnings (y)
$7.50
$15.00
$22.50
$30

7. Finding the Constant of Proportionality Ex. 2
Determine the constant of proportionality.
People (x) 3 5 7 9
Slices of Pizza (y) 15 21 27

8. Finding the Constant of Proportionality Ex. 3
Determine the constant of proportionality.
Cookies (x) 2 3 4 5
Price (y)
$1.00
$1.50
$2.00
$2.50

9. Finding the Constant of Proportionality Ex. 4
Determine the constant of proportionality.
People (x) 5 6 7 8
Slices of Pizza (y)
17.5 21
24.5 28

10. Proportional or Not?
Is the table above showing a proportional relationship? If it is, what is the constant of proportionality.
Input (x) 1 2 3 4
Output (y) 6 8

11. Proportional or Not?
Is the table above showing a proportional relationship? If it is, what is the constant of proportionality.
Input (x) 3 4 5 6
Output (y) 18 24 30 34

12. Proportional or Not?
Is the table above showing a proportional relationship? If it is, what is the constant of proportionality.
Input (x) 2 3 4 5
Output (y)
3.5
5.25 7
8.75

13. Proportional or Not?
Is the table above showing a proportional relationship? If it is, what is the constant of proportionality.
Input (x) 1 2 3 4
Output (y)
6.3
12.6
18.6
25.2

14. Proportional or Not? - Graphs
Two conditions:
Must pass through the origin
Must be a straight line

15. Finding the Constant of Proportionality on a Graph
Find the y value for x = 1.

16. Which of the following graphs show direct variation (proportional relationship)?

17. Graph and find k.
Input (x) 1 2 3 4
Output (y)
1.5
4.5 6

18. Determining Proportional Relationships by the Equations
Must be in the format y = kx
ProportionalNot Proportional
y = 7x y = x - 4
y = 1 3 x y = 2x – 3
What do you notice?

19. Determining Proportional Relationships by the Equations
Must be in the format y = kx
y = 5x YES
y = x – 2 NO
y = 1 2 x YES
y = -9x YES
y = 3x – 4 NO