Lesson 14
TAKS
TAKS
Grade
Grade
9 Objective
# Objective
3 #
(A.5)(A)
(7.2)(#)
Identifying Linear Functions
A function is a relationship between two variables in which each input
value corresponds to exactly one output value.
A linear function is a function whose graph is a line. Situations involving
a constant rate of change can be represented by linear functions. The rate
of change of a linear function is called its slope.
New Vocabulary
• function
• linear function
Finding Equations
When determining whether or not a given situation can be represented
by a linear function, it may be helpful to find an equation that models
the situation.
The word “line” is part
of the word “linear.”
EXAMPLE 1
Quick Check 1
1a. Gordon spends $80 on groceries once a
week, plus $25 on kitchen and cleaning
supplies once every 6 weeks.
Can his spending be represented by a linear
function? Explain.
40
LESSON 14
■
Identifying Linear Functions
1b. At your job, your starting wage is $7.50 an
hour, and you are expected to receive a
raise of 25 cents per hour every six months.
Can your wages be represented as a linear
function? Explain.
TAKS Review and Preparation Workbook
Copyright © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
Last year, a movie ticket cost $6. Today, a movie ticket can be
purchased for $6.50. Theater owners predict that this pattern of
increase in the cost of a movie ticket will continue. Can this situation
be modeled by a linear function?
Look for clues in the statement of the problem that will allow you to
determine whether this situation can be modeled by a linear function.
The pattern of increase is $0.50 per year. This represents a constant rate of change in the
cost of a movie ticket. This problem situation can be modeled by a linear function.
TAKS Objective 3 (A.5)(A)
LESSON 14
Equations and Graphs of Linear Functions
An equation for a linear function can be in the form f(x) mx b or in the
form y mx b.
Linear Function
Linear Function
y 12x 2
yx3
4
y
4
2
–4
Nonlinear Function
y x2 1
y
4
2
–2 O
2
4x
–4
–2 O
y
2
4x
2
–4
–2 O
–2
–2
–2
–4
–4
–4
2
4x
EXAMPLE 2
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A class working on a geometry project listed the lengths of the
sides of the squares they created and compared them to the areas
of the squares.
y
Side Length
Area
1 in.
1 in.2
24
2 in.
4 in.2
18
3 in.
9 in.2
12
4 in.
16 in.2
6
5 in.
in.2
25
O
2
4
6
If you are given a table,
but no equation, you
can try plotting the
points to determine
whether or not a
function is linear. If the
graph is not a line, the
function is not linear.
8 x
Can the data be represented by a linear function?
Graph the data. Check to see if the graph of the function is a line.
This is not a linear function, because it cannot be represented by a line.
Quick Check 2
2a. Your uncle will pay you to mow his lawn
every week. He will either pay you $5 per
week, or he will pay you 1¢ for the first
week, 2¢ for the second week, 4¢ for the
third week, and so on, doubling the previous
amount each time. Which payment plan can
be represented by a linear function? How do
you know?
TAKS Review and Preparation Workbook
2b. You enter a jump rope contest for a charity.
You get pledges for each minute you can
jump rope without stopping. You have
pledges totaling $17 per minute.
Can the relationship between minutes
jumped and money earned be represented
by a linear function? How do you know?
LESSON 14
■
Identifying Linear Functions
41
Name__________________________Class____________Date________
1 Which of the following graphs represents
a linear function?
4
y
H x y 20 2x
O
–4
F x7y
G 21x y
2
A
2 Which function is NOT linear?
–2
2
4x
–2
J y 30 x2
–4
4
3 Which of the following sets of ordered pairs
could NOT be part of a linear function?
y
A (0, 1), (1, 2), (3, 4)
2
B
B (2, 10), (4, 20), (6, 30)
–4
–2 O
2
4x
–2
C (3, 10), (4, 17), (6, 37)
D (3, 6), (5, 10), (7, 14)
–4
4 Which situation CANNOT be represented
by a linear function?
y
2
C
–4
–2 O
2
4x
–2
G A student collects 15 pounds of cans
every 2 weeks for a fundraiser.
–4
4
H A writer uses twice as many pencils each
week as he did the week before.
y
J A teacher writes down a check mark
for every 15 minutes her students
read silently.
2
D
–4
–2 O
F A worker’s monthly earnings include a
bonus of $25 and pay at a rate of $6 per
hour he worked that month.
2
4x
–2
–4
5 Which of the following sets of ordered pairs
can be part of a linear function?
A (1, 1), (12, 2), (2, 12)
B (1, 1), (0, 2), (2, 2)
C (2, 1), (0, 5), (1, 8)
D (3, 9), (2, 8), (5, 125)
42
LESSON 14
■
Identifying Linear Functions
TAKS Review and Preparation Workbook
Copyright © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
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