MATH 10 - UNIT 6 – LESSON 6 – LINEAR RELATIONS & RATE OF CHANGE
FUNCTIONS UNIT
Name:____________ Block: _____ Date: _______
Linear Relation: ______________________________________________________________________
Graphs of Linear Relations
Example: Which of the following graphs represent linear relations?
Note: ______________________________________________________________________________
Table of Values
We can tell just by looking at a table of values whether or not it represents a linear relation!
Example: Determine whether or not the following tables of values represent linear relations.
x
1
2
3
4
5
6
y
5
7
9
11
13
15
x
-6
-4
-2
0
2
4
y
10
7
4
1
-2
-5
x
-3
-2
-1
0
1
2
y
4
7
3
9
1
5
Note: ______________________________________________________________________________
Ordered Pairs
Example: Determine whether or not the following sets of ordered pairs represent linear relations.
6,4, 3,2, 0,0, 3, 2, 6, 4
10, 1, 5,0, 0,1, 10,2
Note: ______________________________________________________________________________
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MATH 10 - UNIT 6 – LESSON 6 – LINEAR RELATIONS & RATE OF CHANGE
FUNCTIONS UNIT
Name:____________ Block: _____ Date: _______
Rate of Change: _______________________________________________________________________
Example: Determine the rate of change of the following linear functions.
Rate of change: ___________
Rate of change: ___________
Linear functions that are slanted up to the right have a __________ rate of change.
Linear functions that are slanted down to the right have a __________ rate of change.
!" !#
$" $#
Example: Determine the rate of change of each of the following linear functions.
Rate of change: ___________
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Rate of change: ___________
MATH 10 - UNIT 6 – LESSON 6 – LINEAR RELATIONS & RATE OF CHANGE
FUNCTIONS UNIT
Name:____________ Block: _____ Date: _______
Equation of a Linear Relation: ! $ % where is the rate of change and is the initial value (or the value of ! when $ 0)
Example: Circle the equations that represent linear relations.
! 9$ % 5
3$ % ! 7
! 3$ "
! √$
2$ 3! % 2 0
! $%)
Example: A taxi charges a flat rate of $5 plus an extra $2 per kilometre.
1. Write an equation to represent the relation between number of km driven & total cost of a taxi ride.
2. Is it a linear relation?
3. What is the rate of change?
4. What is the initial value?
Example: The following set of ordered pairs represents the relation between the number of students
who attended a dance and the profit made. Graph the relation. 0, 500, 100,500, 200,1500
1. Identify the independent / dependent variables.
2. Is this a linear relation? __________
3. What is the rate of change? _______
4. What is the initial value? __________
5. Create an equation to represent the relation.
Lesson 6 Homework: WS 10-6-6 “Linear Relations”
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