Transcript proportional relationship

How can you show an infinite number of possible
answers?
Egg salad: 2 pound for $6
How much is one pound of egg salad? How
about 6 pounds? You can display all the
possibilities in a proportional relationship by
graphing!
1 pound for $5
1 pound for $3
2 pounds for $6
20 pounds
for $100
6 pounds
for $18
Core
Lesson
Let’s
Review
Weight Cost ($)
(lb.)
2
6
4
12
6
18
2 pounds for $6
Core
Lesson
Let’s
Review

Weight (lb.) Cost ($)
(y)
(x)
2
6
4
12
6
18
Cost ($)







Weight (lb.)



Proportional vs. Non-Proportional
• If two quantities are proportional, then
they have a constant ratio.
– To have a constant ratio means two quantities
have the same unit rate.
• If the ratio is not constant, the two
quantities are said to be non-proportional.
– So, the two quantities do not have the same
unit rate.
Proportional Relationships
• Will always go through the origin on a graph.
(0,0)
• Graph will always be a straight line.
In order to tell if a graph is proportional the line must go
through the origin.
Tell if the following graphs represent a
proportional relationships.
y
y
5
5
4
4
3
3
2
2
1
1
x
1
x
1
2
3
4
3
4
5
5
Proportional ? _________
Yes
Why?
2
Line goes through
the origin
No
Proportional ? _________
Why?
Line does not
go through the origin
Core
Lesson
Let’s
Review

Weight (lb.) Cost ($)
(y)
(x)
2
6
4
12
6
18
Cost ($)




Is the weight of the egg
salad proportional to the
cost?



Weight (lb.)
Yes



Guided
Practice
Let’s
Review
Weight (lb.) Cost ($)
(x)
(y)
2
11
1
5.50
4
22

Cost ($)
Graph the proportional
relationship “2 pounds of
prime rib for $11.”








Weight (lb.)
Is the weight of the prime rib proportional to the cost?
Yes


Guided
Practice
Let’s
Review

Distance (ft.)
State in words the
proportional
relationship shown here.
(There are many correct
answers!)
y

2 feet per min
x




Time (min.)



Quick
Quiz
You
Try
Let’s
Review


Cost ($)
State in words the
proportional
relationship shown
here.
(There are many
correct answers!)




5oz for $2










Weight (ounces)



You try: The following chart shows how much money Alex earns for mowing
lawns. Is the amount of money he earns proportional to the number of hours
that he spends mowing?
Earnings Hours
($)
(h)
Unit $Rate
( hr )
1
$14
1
2
$28 $14

2
1
42
3
$42 $14

3
1
56
4
$56 $14

4
1
14
28
Since the simplified ratios were equal,
this was a proportional relationship.
You try: Let’s graph this proportional relationship from Ex. 1 on an
xy-plane.
We typically put time (hours) on the x-axis, and
the earnings ($) on the y-axis.
Set up the graph paper to fit the data in the chart.
Plot points (x, y) from the table.
Point
(x, y)
56
42
1
14
(1, 14)
2
28
(2, 28)
Earnings
($)
Hours Earnings
(h)
($)
y
28
3
42
(3, 42)
4
56
(4, 56)
Connect the points.
Describe the graph of this
proportional relationship.
14
1
2
3
Hours
worked
4
5
x
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
cost ($)
no. of tickets
$10
1
17 $8.5

2
1
$24 $8

3
1
$31 $7.75

4
1
Since all of the simplified ratios are not equal, there is no
constant ratio, so this is NOT a proportional relationship.
Now, let’s graph this nonproportional relationship from Ex. 2.
It passes through the origin,
but it is not a straight line.
Tickets ordered will be on the x-axis,
and the cost ($) will be on the y-axis.
Plot points (x, y) from the table.
Earnings ($) Point (x, y)
0
0
(0,0)
1
10
(1, 10)
2
17
(2, 17)
3
24
(3, 24)
4
31
(4, 31)
Connect the points.
Describe the graph of this
nonproportional relationship.
y
28
Cost ($)
Tickets
32
24
20
16
12
8
4
1
2
3
4
Tickets ordered
x
Practice:
Graphing Worksheet