Post on 18-May-2015
5.6 Linear Relations.notebook
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5.6 Properties of Linear Relations
Linear relations are special types of relations that describe many real life situations...
A linear relations shows a constant change. A constant change in the independent variable results in a constant change in the dependent variable.
5.6 Linear Relations.notebook
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Identifying linear functions using a...
Table of Values
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Identifying linear functions using a...
A Set of Ordered Pairs
{(0, 60), (100, 80), (200, 100), (300, 120), (400, 140)}
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Identifying linear functions using a...
Graph
0 100 200 300 400 500
20
40
60
80
100
120
140
160
x
y
Distance (km)
Cost
($)
Car Rental Cost
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The Rate of Change is the ratio of how fast the change occurs.
rate of change =change in dependent variable
change in independent variable
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We can determine the rate of change from the equation that represents the linear function.
C = 0.20d + 60
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Equations for linear relations are always in the form...
y = mx + b
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I P0 05 7510 30015 67520 1200
The following table shows the relation between the current (I) to the Power (P) in an electrical circuit. Is this a linear relation? Why or why not?
Example 1
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Example 2
Graph y = 4x + 6
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Which of the following are linear relations?
a.) y = 3x + 25
b.) y = 2x2 + 5
c.) y = 5
d.) x = 1
Example 3
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Graph A
Filling a hot tub
Time (min)
Volu
me
(L)
0 20 40 60 80 100
200
400
600
800
1000
1200
1400
1600
x
y
Example 4.
Identify the dependent and independent variables and determine the rate of change for the following scenario.
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Example 4.
Identify the dependent and independent variables and determine the rate of change for the following scenario.
Graph B
Emptying a hot tub
Time (min)
Volu
me
(L)
0 20 40 60 80 100 120
200
400
600
800
1000
1200
1400
1600
x
y
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Graph B
Emptying a hot tub
Time (min)
Volu
me
(L)
0 20 40 60 80 100 120
200
400
600
800
1000
1200
1400
1600
x
y
Graph A
Filling a hot tub
Time (min)
Volu
me
(L)
0 20 40 60 80 100
200
400
600
800
1000
1200
1400
1600
x
y
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