Identifying
and
Representing
Proportional
Relationships
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?
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.
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.
Finding the Constant of Proportionality
• To find k you must divide the y value
by the x value.
Finding the Constant of
Proportionality Ex. 1
Hours Worked (x)
1
2
Total Earnings (y)
$7.50
$15.00 $22.50 $30
3
4
• Determine the constant of proportionality.
Finding the Constant of
Proportionality Ex. 2
People (x)
3
5
7
9
Slices of Pizza (y)
9
15
21
27
• Determine the constant of proportionality.
Finding the Constant of
Proportionality Ex. 3
Cookies (x)
2
3
4
5
Price (y)
$1.00
$1.50
$2.00
$2.50
• Determine the constant of proportionality.
Finding the Constant of
Proportionality Ex. 4
People (x)
5
6
7
8
Slices of Pizza (y)
17.5
21
24.5
28
• Determine the constant of proportionality.
Proportional or Not?
Input (x)
1
2
3
4
Output (y)
2
4
6
8
• Is the table above showing a proportional
relationship? If it is, what is the constant of
proportionality.
Proportional or Not?
Input (x)
3
4
5
6
Output (y)
18
24
30
34
• Is the table above showing a proportional
relationship? If it is, what is the constant of
proportionality.
Proportional or Not?
Input (x)
2
3
4
5
Output (y)
3.5
5.25
7
8.75
• Is the table above showing a proportional
relationship? If it is, what is the constant of
proportionality.
Proportional or Not?
Input (x)
1
2
3
4
Output (y)
6.3
12.6
18.6
25.2
• Is the table above showing a proportional
relationship? If it is, what is the constant of
proportionality.
Proportional or Not? - Graphs
• Two conditions:
–Must pass through the origin
–Must be a straight line
Finding the Constant of
Proportionality on a Graph
30
25
20
15
10
5
0
0
1
2
Find the y value for x = 1.
3
4
5
6
Which of the following graphs show direct
variation (proportional relationship)?
Graph and find k.
Input (x)
1
2
3
4
Output (y)
1.5
3
4.5
6
Determining Proportional
Relationships by the Equations
• Must be in the format y = kx
ProportionalNot Proportional
y = 7x
y=x-4
y=
1
x
3
What do you notice?
y = 2x – 3
Determining Proportional
Relationships by the Equations
• Must be in the format y = kx
1. y = 5x
2. y = x – 2
3. y =
1
x
2
4. y = -9x
5. y = 3x – 4
YES
NO
YES
YES
NO