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Objective
Graph linear equations
Vocabulary
Function
A relationship where one thing depends on
another
Vocabulary
Function table
An organized method of the input numbers,
output numbers, and the function rule
Input
Domain
Function
Rule
Output
Range
Vocabulary
Domain
The set of input values
Vocabulary
Range
The set of output values
Vocabulary
Linear equation
An equation, when graphed, forms a straight
line
Review
Vocabulary
Ordered pair
A pair of numbers used to locate a point in a
coordinate system
Example 1 Make a Function Table
Example 2 Graph Solutions of Linear Equations
Example 3 Represent Real-World Functions
WORK Asha makes $6.00 an hour working at a grocery
store. Make a function table that shows Asha’a total
earnings for working 1, 2, 3, and 4 hours.
Make a function table
Label columns
Input
Output
Function
1/3
$6.00 an
an hour
hour working at a grocery
WORK Asha makes $6.00
store. Make a function table that shows Asha’a total
total
earnings for working 1, 2, 3, and 4 hours.
hours
Identify the input
Input
Number of
Hours
Identify the function
Identify the function
Function
Output
Multiply by 6
Total
Earnings
($)
1/3
WORK Asha makes $6.00 an hour working at a grocery
store. Make a function table that shows Asha’a total
hours
earnings for working 1, 2, 3, and 4 hours.
Put number of hours in the input column
Input
Number of
Hours
Function
Output
Multiply by 6
Total
Earnings
($)
1
2
3
4
1/3
WORK Asha makes $6.00 an hour working at a grocery
store. Make a function table that shows Asha’a total
earnings for working 1, 2, 3, and 4 hours.
Multiply the input by 6 to find the output
Input
Number of
Hours
1
2
3
4
Function
Output
Multiply by 6
Total
Earnings
($)
16
26
36
46
6
12
18
24
1/3
WORK Asha makes $6.00 an hour working at a grocery
store. Make a function table that shows Asha’a total
earnings for working 1, 2, 3, and 4 hours.
Answer:
Input
Number of
Hours
1
2
3
4
Function
Output
Multiply by 6
Total
Earnings
($)
16
26
36
46
6
12
18
24
1/3
MOVIE RENTAL Dave goes to the video store to rent a
movie. The cost per movie is $3.50. Make a function
table that shows the amount Dave would pay for renting
1, 2, 3, and 4 movies.
Answer:
Input
Function Rule
Output
Number of
Movies
Multiply by 3.50
Total
Cost ($)
1
3.50  1
3.50
2
3.50  2
7.00
3
3.50  3
10.50
4
3.50  4
14.00
1/3
Make a table with 4 columns
Label 1st column as “x”
Graph
Label 2nd column with the rule
Label 3rd column as “y”
x
x+3
y
2/3
Label 4th column as the ordered
pairs (x, y)
Graph
Select any four values for the
input x
x
x+3
y
(x, y)
2
2+3
5
(2, 5)
1
1+3
4
(1, 4)
0
0+3
3
(0, 3)
-1
-1 + 3
2
(-1, 2)
I choose 2, 1, 0, and -1
because they are small and
easy
Substitute the value of x into
the function column
Make the ordered pairs from
the x and y columns
2/3
(2, 5)
Graph
Graph the ordered pairs
Label ordered pairs
(1, 4)
(0, 3)
(–1, 2)
x
x+3
y
(x, y)
2
2+3
5
(2, 5)
1
1+3
4
(1, 4)
0
0+3
3
(0, 3)
-1
-1 + 3
2
(-1, 2)
2/3
(2, 5)
Graph
Draw a line connecting the
dots
(1, 4)
(0, 3)
(–1, 2)
x
x+3
y
(x, y)
2
2+3
5
(2, 5)
1
1+3
4
(1, 4)
0
0+3
3
(0, 3)
-1
-1 + 3
2
(-1, 2)
2/3
(2, 5)
Graph
(1, 4)
Answer:
(0, 3)
(–1, 2)
x
x+3
y
(x, y)
2
2+3
5
(2, 5)
1
1+3
4
(1, 4)
0
0+3
3
(0, 3)
-1
-1 + 3
2
(-1, 2)
2/3
Graph
Answer:
Ordered pairs will vary depending on
your choice for x but the line should
be alike
2/3
ANIMALS Blue whales can reach a speed of 30 miles per
hour in bursts when in danger. The equation
describes the distance d that a whale traveling at that
speed can travel in time t. Represent this function with a
graph.
Draw a function table
t
30t
d
with 4 columns
Label the 1st column
with t for time
Label the 2nd column
with the rule
Label the 3rd column
with the output for
distance d
3/3
ANIMALS Blue whales can reach a speed of 30 miles per
hour in bursts when in danger. The equation
describes the distance d that a whale traveling at that
speed can travel in time t. Represent this function with a
graph.
Label 4th column with
t
30t
d
(t, d)
the ordered pairs
1
2
3
Choose 4 values for
the time
I choose 1, 2, 3, and
4 hours because
they are easy to
graph
4
3/3
ANIMALS Blue whales can reach a speed of 30 miles per
hour in bursts when in danger. The equation
describes the distance d that a whale traveling at that
speed can travel in time t. Represent this function with a
graph.
Substitute the input
t
30t
d
(t, d)
of t into the function
1
30  1
30
(1, 30)
Find the output d
2
30  2
60
(2, 60)
3
30  3
Make ordered pairs
from the t and d
columns
90
(3, 90)
4
30  4
120
(4, 120)
3/3
Graph the ordered pairs
Label the horizontal axis
Label the vertical axis
140
Scale must include
0 - 120
120
100
80
60
40
20
t
1
30t
30(1)
d
30
(t, d)
(1, 30)
2
3
4
30(2) 60
30(3) 90
30(4) 120
(2, 60)
(3, 90)
(4, 120)
1 2 3 4
3/3
Plot each ordered pair
Draw a line through the points 140
120
Answer:
100
80
t
30t
d
(t, d)
60
1 30(1) 30 (1, 30)
40
20
2 30(2) 60 (2, 60)
3 30(3) 90 (3, 90)
4 30(4) 120 (4, 120)
(4, 120)
(3, 90)
(2, 60)
(1, 30)
1 2 3 4
3/3
*
TRAVEL Susie takes a car trip traveling at an average
speed of 55 miles per hour. The equation
describes the distance d that Susie travels in time t.
Represent this function with a graph.
Answer:
3/3
Assignment
Functions and Linear
Lesson 4:6
Equations
8 - 25 All