Name: ____________________________________
Date: __________________
WORKING WITH LINEAR FUNCTIONS IN TABLE FORM
N-GEN MATH® ALGEBRA I
We have now worked with linear functions in both equation form and graph form. In this lesson, we will look at
linear functions in table form.
Exercise #1: Values for a linear function are shown in the table below.
(a) Plot the information in the table on the grid
provided and draw the linear function.
(b) What is the change in x from one row in the
table to the next row?
(c) What is the change in y from one row in the
table to the next row?
(d) Use your answers from (b) and (c) to determine
the slope of the line.
x
y
3
3
0
5
3
7
6
9
(e) What is the y-intercept of the line? How can you
tell from the table?
One of the key features of all linear functions can be seen in tables as long as the x-values change by equal
amounts (known as equal domain intervals).
FUNDAMENTAL CHARACTERISTIC OF A LINEAR FUNCTION
The outputs (or y-values) of linear functions will change by equal differences for equal changes in the x-values.
Exercise #2: For each of the following tables, where the x-values change by equal amounts, determine if the table
could represent a linear function. Justify.
(a)
®
x
y
0
(b)
(c)
x
y
3
2
0
5
16
4
21
8
(d)
x
y
7
8
13
3
4
5
6
8
8
1
2
1
12
13
2
1
8
x
y
6
4
2
11
4
6
N-GEN MATH® ALGEBRA I – UNIT 4 – LINEAR FUNCTIONS – LESSON 4
eMATHinstruction, RED HOOK, NY 12571, © 2022
®
Exercise #3: The function f  x  is linear. Some of its values have been filled into the table below.
x
4
f  x
19
2
0
2
4
4
(a) Determine the slope (average rate of change) for
this linear function.
(b) For every two units of increase in the x-value,
what happens to the y-value?
(c) Fill in the table and write an equation for this
linear function in y  mx  b form.
(d) What is the value of f  20  ?
It is important to be able to compare linear functions that come in different forms. The most important of which
are equation, graph, and table forms.
Exercise #4: Three functions are shown below in various forms. All three functions have both positive slopes
and positive y-intercepts.
(a) Which of the three functions has the largest
y-intercept? Justify.
x
g  x
2
8
0
11
2
14
4
17
6
20
8
23
(b) Which function has the largest slope?
Justify.
®
N-GEN MATH® ALGEBRA I – UNIT 4 – LINEAR FUNCTIONS – LESSON 4
eMATHinstruction, RED HOOK, NY 12571, © 2022
®
Name: ____________________________________
Date: __________________
WORKING WITH LINEAR FUNCTIONS IN TABLE FORM
N-GEN MATH® ALGEBRA I HOMEWORK
FLUENCY
1.
Values of a linear function are shown in the table below. Which of the following is the slope of the linear
function?
x
y
5
5
(1) 
(3)
5
15
3
3
(2) 
2.
3
5
(4)
3
5
0
12
5
9
10
6
Which of the following would be the equation of the linear function shown in the table below?
1
(1) y   x  6
2
(2) y  2 x  4
(3) y  2 x  6
x
y
4
6
2
5
0
4
2
3
1
(4) y  x  4
2
3.
4.
If the values below represent a linear function, which of the following would be its y-intercept?
(1) 3
x
y
(2) 2
2
2
(3) 5
2
8
(4) 6
6
14
10
20
Which table below could not represent a linear function?
(1)
®
x
y
0
(2)
x
y
5
1
1
10
2
3
(3)
x
y
7
2
0
3
20
1
40
2
(4)
x
y
10
4
3
1
8
6
2
1
4
6
8
7
5
7
4
10
12
N-GEN MATH® ALGEBRA I – UNIT 4 – LINEAR FUNCTIONS – LESSON 4
eMATHinstruction, RED HOOK, NY 12571, © 2022
®
5.
Two linear functions are shown below, one in table form and one in graph form.
x
f  x
1
13
0
8
1
3
2
2
3
7
4
12
Which of these two functions will have the greater output for an input of x  10 ? Justify your answer.
APPLICATIONS
6.
A weather balloon is carrying instruments into the atmosphere to measure various parameters. The height of
the weather balloon is recorded for the first five seconds of its rise into the air. The data is shown in the table
below.
t (seconds)
0
1
2
3
4
5
h (ft)
27
42
57
72
87
102
(a) How does the data in the table indicate that the
height of the balloon is a linear function of time?
(b) What is the average rate of change of the height?
Include proper units.
(c) Give a formula for the height, h, as a linear
function of the time, t, it has been in the air.
(d) How high above the ground does your model
from (c) predict the balloon will be after 5
minutes of rising?
®
N-GEN MATH® ALGEBRA I – UNIT 4 – LINEAR FUNCTIONS – LESSON 4
eMATHinstruction, RED HOOK, NY 12571, © 2022
®