Download - Constant of Proportionality
Constant of Proportionality
7th GradeChapter 2
CC.7.RP.2b Identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Standard
How do I identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships?
Essential Question
Remember:Unit Rate is…
A ratio that has a denominator of one… showing the value of one unit.
Examples: price per pound pages read in one hour cups that can fit on one
shelf price per gallon
Real World Application
If a person walks 4 mile in 2 hours, what is the unit rate? (miles per hour)
=
2 miles per hour
Xindependent
Ydependent
Record your information in a table.
Books Price
1 5
2 10
3 15
4 20
5 25
6 30
The independent variable does not depend on anything.
The dependent variable depends on the independent variable in order to find its value.
Graph It!
independentdepend
ent
BooksPri
ce1 2 3 4 5
123456
8
10
7
9A straight line through the origin shows a direct proportion on a graph…
As x is increasing, y is also increasing.
Proportionality
The graph of a proportional relationship is a straightline that passes through the origin.
Proportional quantities can be describedby the equation y = kx, where k is a constant ratio... also known as constant of proportionality.
Xindependent
Ydependent
Using the form y = kx, write an equation for the information in the
chart.
Books Price
1 5
2 10
3 15
4 20
5 25
6 30
What did you multiply x to get y?
5x = y
Xindependent
Ydependent
Books Price
1 5
2 10
3 15
4 20
5 25
6 30
5x = y
If y = kx then doesn’t k = y/x?
To find the constant of proportionality, you can divide the y coordinate by the x coordinate.
5/1 = 510/2=515/3=520/4=525/5=530/6=5
The constant of proportionality is 5.
Constant of Proportionality
Do you remember where the 5 came from? The unit rate…it is the number that you used to multiply by each x value to get each y value.
Unit rate is also known as the constant of proportionality because it is the number that remains constant in each proportional situation.
Write the unit rate:
Read 80 pages in 2 hours_______ pages in one hour40
X Y
Record your information in the table.
Hours Pages
1 40
2 80
3 120
Is this a direct proportion?Yes…as x increases by the same rate, by y increases by the same rate.
What is the constant of proportionality?k= =
40
Which is the dependent variable?
independent dependent
Which is the independent variable?
Graph It!
independent
depend
ent
HoursPa
ges
102030405060708090
100
1 2 3 4 5
How do you determine if the graph is a direct proportion?
A straight line through the origin shows a direct proportion.
Write the unit rate:
A plane travels 2250 km in 3 hours. What is the average speed? (km per hour)
750 km/hrWhat is the constant of proportionality?
They are asking for unit rate…
750
Graph It!
independent
depend
ent
Hours
Km
250
500
750
1000125015001750200022502500
1 2 3 4 5
Is this a direct proportion?
Yes…A straight line through the origin shows a direct proportion.
k = y/xk = 20/2k = 10
Find the first point on the graph and name it using the form (x,y).
(2, 20)
x
y
Plug those into the formula to find the constant of proportionality.
k = 2 Write the equation for the graph above. y = 2x
Write an equation for the information in the table.
X y
1 10
2 20
3 30
4 40
5 50
y = 10x
What is the constant of proportionality? 10
k = 5Write the equation for the graph above. y = 5x
k = 7.5Write the equation for the graph above. y = 7.5x
Y = 12/x
No. The equation is not in the form y = kx.
k = 12.5
Closing
How do you find the constant of proportionality from a:Ratio?Table?Equation?Graph?
How do you determine if the proportional relationship shown is a direct proportion in a:
Table?Graph?