1. Proportional Relationships
Unit 3 ~ Lesson 4B
Proportional Relationships

2. Warm-up
Solve

3. Proportional Relationships are represented in the following ways:
Verbal Descriptions
Equations
A truck travels at a constant rate of speed and is traveling 50 miles every hour. How far would it travel in 5 hours?
d = 50t d = total distance
r = 50 mph
t = hours driven
Tables
Time t (hours) 1 2 …. 5
Distance d (in miles) 50
100 ?
x - axis
y - axis y 2 4 50
100
150 x
Miles
Hours 6 8
200
250
300
Graphs
Use the data
from the table
to plot the
coordinates.
(x, y)
Distance is on the y - axis
Time is on the x - axis

4. Now solve the problem for distance traveled in 5 hours.
Verbal Descriptions
Solution:
50 miles • 5 hours
A truck travels at a constant rate of speed and is traveling 50 miles every hour. How far would it travel in 5 hours?
= 250 miles
Equations
d = 50t d = total distance
r = 50 mph
t = hours driven
d = 50 miles • 5 hours
d = 250 miles

5. Now solve the problem for distance traveled in 5 hours.
Tables
Time t (hours) 1 2 …. 5
Distance d (in miles) 50
100 ?
x - axis
250
y - axis
Reading the table: what did you multiply “ x ” by to get “ y ”?
x • 50
So multiply 5 by 50 y 2 4 50
100
150 x
Miles
Hours 6 8
200
250
300
Graphs
Use the data
from the table
to plot the
coordinates.
(x, y)
Reading the graph: locate 5 hours on the x-axis and
estimate the number of miles based on the graph.

6. Verbal Descriptions & Equations
You can use an equation to represent a verbal description of a proportional relationship.
Equation Format: y = kx
k is the constant of proportionality or unit rate
Amy charges $10 an hour to babysit.
Write an equation in this format: y = kx
y = total
k = constant of proportionality (unit rate)
x = quantity
Assign values
to the variables
y = total $ earned k = hourly rate x = time (hours)
Equation:
y = x  $10 or
y = $10x or
c = $10h
So what is the constant of proportionality again?
Recall the first example: d = 50t
It was also written in the same format: k is the UNIT RATE because it is 50 miles per hour
It is the constant rate of change or UNIT RATE: $10 per hour

7. Equations & Constant of Proportionality
Write an equation for each situation below & identify the constant of proportionality. Equation Format: y = kx
y = total
k = constant of proportionality (unit rate)
x = quantity
Assign values
to the variables
The football ticket cost is $7.
The state playoff football ticket cost $12.
Andrew charges $9.50 an hour to cut grass.
For these equations to be
directly proportional,
k & x must be multiplied!
y =
k =
x =
total ticket sales $7
# of tickets sold
y = $7x
y =
k =
x =
total ticket sales
$12
# of tickets sold
y = $12x
y =
k =
x =
total income
$9.50
# of hours worked
y = $9.5x

8. Equations & Constant of Proportionality
Write an equation for each situation below & identify the constant of proportionality. Equation Format: y = kx
y = total
k = constant of proportionality (unit rate)
x = quantity
Assign values
to the variables
4. My car gets 26 miles per gallon.
5. The height of the building is equal to the number of floors times 12 feet.
6. Write your own situation that could be represented by the equation y = 35x. State what x, y, and 35 represent in your problem and explain how you know that the problem represents a proportional relationship.
For these equations to be
directly proportional,
k & x must be multiplied!
y =
k =
x =
total distance 26
# of gallons of gas
y = 26x
y =
k =
x =
total height of the building 12
# of floors
y = 12x

9. Name the Constant of Proportionality
7. y = -9x x = y y = -x

10. Tables
10. This table displays the rate at which water is flowing from a faucet into a
bathtub.
Write an equation. _________________
How many gallons are in the bathtub in 4 minutes? ______
How many gallons of water would be in the bathtub in10 minutes? _______
Does it have a proportional relationship? ________ Why or Why Not?
Time m (minutes) 1 2 3 4
Gallons g (in gallons) 6 ?
x - axis
y - axis
*Assign x and y values on the table
*What did you multiply “ x ” by to get “ y ”?

11. Tables A cheetah runs 87 meters in 3 seconds.
Write an equation. ______________
How far can it run in 10 seconds? _____
How far can it run in 1second? _______
Does it have a proportional relationship? ________ Why or Why Not?
Time s (seconds) 3 4 5 …. 10
Distance m (in meters) 87
116
145 ?

12.      Tables & Graphs…..complete the table & graph the results 12.
Time m (minutes) 1 2 3 4
Gallons g (in gallons) 6 ?
x - axis 8
y - axis
Gallons
Minutes 2 4 6 8 10
Which point on the graph shows the unit rate? 
HINT: When x is 1, y is the unit rate. 
(1, 2) 
What is the unit rate?  2 

13. Tables & Graphs…..complete the table & graph the results
13.
Time s (seconds) 3 4 5 …. 10
Distance m (in meters) 87
116
145 ?
x - axis
290
y - axis 
Meters
Seconds 29 58
116
174
232 2 4 6 8 10 87
145
202
261
290
Which point on the graph
shows the unit rate?
(1, 29)  
What is the constant
of proportionality?   29   

14.     Tables & Graphs…..complete the table & graph the results
14. The equation y = 7.50x relates to the number of hours worked at Ingles and
the total amount of money earned. Use this equation to complete the
table below.
Time h (hours) 1 2 3 4 5 6
Income d (in dollars)
7.5 15
22.5 30
37.5 45
Income
Hours 10 20 30 40 50 2 4 6 8 
What does the point
(4, 30) represent?
In 4 hours, you will
earn $30   

15. Proportional Relationships
A graph shows a directly proportional relationship if it is linear (straight line)
that passes through or touches the origin (0,0).
Do the graphs below show a proportional relationship?
15.
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