Name:_________________________________
Accordino-Math 7
M1AL11
Date:_________
Period:________
Lesson 11: Constant of Proportionality and
the Equation Y=kx.
Bellringer
a. Comple the chart where the quantities represent a proportional relationship.
Speed in Kilometers (x)
80
Time in Hours (y)
240
100
300
120
420
b. What is the constant of proportionality?
Name:_________________________________
M1AL11
Date:_________
Accordino-Math 7
Period:________
Lesson 11: Constant of Proportionality and the Equation Y=kx.
Notes
A Directly Proportional Relationship has a linear equation of the form
y  kx
Y is the dependent variable, x is the independent variable and k is the _______________________________________.
The ratio
Y
is called the _________________ _______________________________ and represented by the variable
X
K.
Determine if each of the following equations represent a proportional relationship and if so identify the constant of
proportionality.
y  5x
y
y  5x  1
1
x
2
y  2.3x
y
3
x6
4
Example 1:
Given that the following table is in a proportional relationship find the constant of proportionality and write a linear
equation that represents the relationship.
Time
2
4
6
8
Distance
16
32
48
64
What is the Constant of Proportionality? ____________________________
Linear Equation = _________________________________
Name:_________________________________
M1AL11
Accordino-Math 7
Date:_________
Period:________
Example 2:
The graph below shows the number of vertical jumps Ava can do over time.
Is there a proportional relationship? How do you
know?
What is the Constant of
Proportionality?________________________
Linear Equation =
___________________________________________
What does the point (14, 140) mean?
Example 3:
An empty swimming pool is being filled at a rate of 5 gallons per minute. Make a table to display the amount of water in
the pool for the first 6 minutes.
Constant of Proportionality = ____________________________
Linear Equation = _________________________________
Represent the above information on a graph.
What does the point (0 , 0) mean?
What does the point (3, 15) mean?
Name:_________________________________
M1AL11
Date:_________
Accordino-Math 7
Period:________
Homework:
For questions 1 and 2 the tables represent proportional relationships:
a. Determine the constant of proportionality
b. Write an equation
c. Find the missing values to complete the table
1)
x
y
20
80
40
160
60
400
2)
x
1
6
1
4
8
3
y
2
3
1
16
2
20
12
10
3) The graph represents the number of miles Mike ran over time.
a. Construct a table showing the relationship between
the miles ran over time.
Hours
Miles
b. What is the constant of proportionality?
c. Write a linear equation that represents the proportional relationship.
d. How long would it take Mike to run a marathon, which is 26.2 miles? What point would that be located at on the
graph? Plot the point.
e. What does the point at the origin (0,0) mean in terms of the miles ran over time.
Name:_________________________________
M1AL11
Accordino-Math 7
Date:_________
Period:________
Lesson 11: Constant of Proportionality and the
Equation Y=kx.
Exit Ticket
The graph below shows the number of dollars earned to hours worked.
a.
Is there a proportional relationship? How do you
know?
b.
What is the Constant of
Proportionality?________________________
c.
Linear Equation =
___________________________________________