Transcript Constant of Proportionality

PROPORTIONAL VS.
NON-PROPORTIONAL
Sunday, April 12, 2015
REVIEW KEY VOCABULARY



Proportional – when two quantities that simplify to
the same ratio.
Constant – a quantity having a value that does not
change or vary.
Constant of Proportionality - a constant value of
the ratio of two proportional quantities.
PROPORTIONALITY
 Two
quantities are directly proportional if
they have a constant ratio
.
 The
change in one variable is always
accompanied by a change in the other.
 This
constant ratio is called the “constant
of proportionality”. The constant of
proportionality can never be zero.
PROPORTIONAL RELATIONSHIPS
Identify the constant of proportionality:




The constant of proportionality is the unit rate
From the table, look at the ratio of y to x
From the graph, look at the steepness of the graph or look
for the y-value where x is one
From the equation, look for the coefficient of x
PROPORTIONAL VS. NON-PROPORTIONAL
 Two
quantities are directly proportional if
they have a constant ratio y .
x
 If
the ratio is not constant, the two
quantities are non-proportional.
 We
will look at tables, graphs, equations,
and ordered pairs to determine if the
relationship between the variables is
proportional.
EQUATIONS:



You should also be able to write equations to describe
the relationships.
If the situation is proportional, you will use your
constant of proportionality in your equation.
Be sure to define your variables!!!
PROPORTIONAL RELATIONSHIPS: TABLES
 In
order to tell from a table if there is a
proportional relationship between the
variables, you should check to see if the
ratio y is the same for all values in the
x
table.
y
 The ratio x is also known as the scale
factor.
 Reduce or divide to find the constant of
proportionality (unit rate) that defines the
relationship between the variables.
Determine if the tables below represent a proportional
relationship.
Number
of books
(x)
Price
(y)
1
3
3
y
x
Pounds
(x)
Cost
(y)
4
$1
9
6
$1.50
4
12
8
$2
7
18
10
$2.50
y
x
Proportional? ________
Proportional? ________
Ratio __________
Ratio __________
Equation ___________
Equation ___________
Const of Prop __________
Const of Prop __________
Proportional? ________
Ratio __________
Equation ___________
Const of Prop __________
Proportional? ________
Ratio __________
Equation ___________
Const of Prop __________
Proportional? ________
Ratio __________
Equation ___________
Const of Prop __________
PROPORTIONAL RELATIONSHIPS: GRAPHS
 The
graph of a proportion will always be a
straight line that passes through the
origin (0,0).
 Always
write the constant ratio in the
form of y .
x
A Common Mistake
Graph of a Proportional Relationship:
Determine if the graphs below represent a
proportional relationship.
y
y
5
5
4
4
3
3
2
2
1
1
x
x
1
2
3
4
5
1
2
3
4
5
Proportional? _________
Why?
Line goes thru the
origin
Proportional? _________
Why?
Line does not
go thru the origin
Core Lesson
What is the constant of proportionality?
200
(4,180)
(3,135)
Miles
150
(2,90)
100
(1,45)
50
(0,0)
0
0
1
2
3
Hours
4
5
Core Lesson
y
45
90
x
1
2
135
3
200
4
(4,180)
(3,135)
150
Miles
180
(2,90)
100
(1,45)
50
(0,0)
0
0
1
2
3
Hours
4
5
Proportional?
How can You determine the unit rate from a graph?
Constant of proportionality?
Equation?
Proportional?
How can You determine the unit rate from
a graph?
Constant of proportionality?
Equation?
Proportional?
How can You determine the unit rate from
a graph?
Constant of proportionality?
Equation?
PROPORTIONAL RELATIONSHIPS:
EQUATIONS
Determine if the following equations show a
proportional relationship.
Substitute a zero for x in the equation and then solve.
If y then equals zero, then the equation represents a
proportional relationship because the graph of the line
goes through the origin.
y = 3x – 1
y = 10x