November 03, 2014
2-2
Proportional Relationships, Tables, and
Equations
November 03, 2014
Essential Question:
How can you use tables and equations to
identify and describe proportional
relationships?
November 03, 2014
Discovering proportional relationships
A giant tortoise moves at a slow but steady pace. It takes
the tortoise 3 seconds to travel 10.5 inches.
Use the bar diagram to help determine how fast it goes in
one second. What operation did you use to find your
answer?
November 03, 2014
November 03, 2014
Complete the table:
Time
(sec)
1
2
3
4
5
Distance
(in)
Find the ratio of
distance to time.
Write each ratio
in simplest form.
What do you notice about the ratios?
How do you think the distance a tortoise travels is related to time?
November 03, 2014
Suppose the tortoise travels for 12 seconds. Explain how you
could find the distance the tortoise travels.
How would you describe the rate or speed at which the tortoise
travels?
November 03, 2014
PROPORTIONAL relationship is a
relationship between two quantities in
which the ratio of one quantity to another is
constant.
November 03, 2014
Alberto types 45 words per minute. Is the relationship between the
number of words and the number of minutes a proportional
relationship? Why or why not?
Time
(min)
1
2
3
Number
45
of words
Compete the ratios of
words
minutes
constant
the ratios are __________
45
The common ratio is :__________
proportional
So the relationship is ___________
4
5
November 03, 2014
The table shows the distance Allison drove on each day of her
vacation. Is the relationship between the distance and the time a
proportional relationship? Why or why not?
Time(h)
1
Distance
65
(mi)
2
3
4
5
120
195
220
300
Do you think Allison drove at a constant speed for the entire
trip? Why or why not?
November 03, 2014
Equations for proportional relationships:
y = ax
November 03, 2014
Two pounds of cashews cost $5, 3 pounds of cashews cost $7.50, and
8 pounds of cashews cost $20. Show that the relationship between
the number of pounds of cashews and the cost is a proportional
relationship. Then, write the equation for that relationship.
a) table
pounds
2
cost ($)
5
3
b) ratios
2.5
The common ratio is: _______
c) Write the equation:
8
November 03, 2014
How can you use substitution to check your equation?
What is the unit cost (unit rate) for the cashews? How does the unit
cost appear in your equation?
How can you use your equation to find the cost of 6 pounds of
cashews?
November 03, 2014
Journal:
1)How can you use tables and equations to identify and
describe proportional relationships?
2) Create a graphic organizer like the one below to show
how we can use tables and equations to model
proportional relationships. We will be adding to it in the
coming sections.
words
equation
proportional
relationships
table
Graph