What is best?
20oz popcorn for $4.50 or 32 oz popcorn for $7.00 ?
$4.50 / 20 = $0.225 per oz so $0.23
Here is the Unit Cost:
$7.00 / 32 = $0.21875 per oz so $0.22
So the lowest Unit Price (and the best bargain) is 32oz for $7.00
Bell Work
How can you show an infinite number of possible answers?
Egg salad: 2 pound for $6
You can display all the possibilities in a proportional relationship by graphing!
1 pound for $5
2 pounds for $6
20 pounds for $100
1 pound for $3
6 pounds for $18
Proportional vs. Non-Proportional• If two quantities are proportional, then
they have a constant ratio.
• If the ratio is not constant, the two quantities are said to be non-proportional.
Proportional Relationships• Will always go through the origin on a graph.
(0,0)• Graph will always be a straight line.• Always write the constant ratio in the form of
• Reduce or divide to find the constant ratio.
y
x
In order to tell if a graph is proportional the line must go through the origin.
Tell if the following graphs represent a proportional relationships.
1 2 3 4 5
1
2
3
4
5
x
y
1 2 3 4 5
1
2
3
4
5
x
y
Proportional ? _________ Proportional ? _________
Why?Line goes thru the origin
Why? Line does notgo thru the origin
Yes No
Let’s Review
Core Lesson
Weight (lb.)(x)
Cost ($)(y)
2
4
6
6
12
18
Weight (lb.)Is the weight of the potato salad proportional to the cost? Yes
Let’s Review
Core Lesson
Time (hr.)
Graph the proportional relationship “45 miles in 3 hours.”
Time (hr.)(x)
Distance (mi.)
(y)453
1 15
2 30
Is the time proportional to the distance driven? Yes
Let’s ReviewGuided Practice
Graph the proportional relationship “2 pounds of prime rib for $11.”
Weight (lb.)
Weight (lb.)(x)
Cost ($)(y)
112
1 5.504 22
Is the weight of the prime rib proportional to the cost? Yes
Let’s ReviewGuided Practice
State in words the proportional relationship shown here.(There are many correct answers!)
x
y
Time (min.)
2 feet per min
Let’s ReviewExtension Activities
Graph “a loss of 2 dollars per day.” Discuss why the graph is in the fourth quadrant.
Day
Day $
1
3
5
-2
-6
-10
You try: The following chart shows how much money Alex earns for mowing lawns. Is the amount of money he earns proportional to the number of hours that he spends mowing?
Earnings ($)
Hours (h)
Unit Rate ( )
14 1
28 2
42 3
56 4
1
$14
2
$28
1
$14
3
$42
1
$14
4
$54
Since the simplified ratios were equal, this was a proportional relationship.
hr
$
1
$14
We typically put time (hours) on the x-axis, and the earnings ($) on the y-axis.
Set up the graph paper to fit the data in the chart.
You try: Let’s graph this proportional relationship from Ex. 1 on an xy-plane.
x
y
Hours worked
Earn
ings
($
)
1
14
28
42
56
2 3 4 5
Hours (h)
Earnings ($)
Point (x, y)
1 14 (1, 14)
2 28 (2, 28)
3 42 (3, 42)
4 56 (4, 56)
Plot points (x, y) from the table.
Connect the points.
Describe the graph of this proportional relationship.
The graph of a proportional relationship:•is a straight line, AND •it passes through the origin, or point (0,0).
Example 2: Ticket Express charges $7 per movie ticket plus a $3 processing fee per order. Is the cost of an order proportional to the number of tickets ordered? Explain .
Cost ($) 10 17 24 31
Tickets Ordered 1 2 3 4
1
$10
ticketsof no.
($)cost 1
$8.5
2
17
1
$8
3
$24
1
$7.75
4
$31
Since all of the simplified ratios are not equal, there is NOT a proportional relationship
between cost and the number of tickets ordered.
Tickets ordered will be on the x-axis, and the cost ($) will be on the y-axis.
x
y
Tickets ordered
Cost
($)
1
4
24
32
2 3 4
Tickets
Earnings ($)
Point (x, y)
1 10 (1, 10)
2 17 (2, 17)
3 24 (3, 24)
4 31 (4, 31)
Plot points (x, y) from the table.
Connect the points.
Describe the graph of this nonproportional relationship.
Now, let’s graph this nonproportional relationship from Ex. 2.
8
12
16
20
28
This graph shows a nonproportional relationship.
It is a straight line, but it does not pass through the origin.