Functions Worksheet - Big Ideas Math Prealgebra: A Florida Standards Curriculum Teaching Edition Page 20
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47Lesson
6.3
Lesson Tutorials
A linear function is a function whose graph is a nonvertical line. A linear
Key Vocabulary
function can be written in the form y = mx + b, where m is the slope and
linear function,
b is the y-intercept.
p. 258
Writing a Linear Function Using a Graph
1 1
EXAMPLE
Use the graph to write a linear function that relates y to x.
The points lie on a line. Find the slope by
y
(4, 3)
3
using the points (2, 0) and (4, 3).
2
3 − 0
change in y
3
1
m =
=
=
—
—
—
(2, 0)
4 − 2
change in x
2
3
2
1
1
2
3
4
x
Because the line crosses the y-axis at (0, −3),
2
(0,
3)
the y-intercept is −3.
3
4
3
So, the linear function is y =
x − 3 .
—
5
( 2,
6)
2
6
Writing a Linear Function Using a Table
2 2
EXAMPLE
Use the table to write a linear function
−3
−2
−1
x
0
that relates y to x.
y
9
7
5
3
y
( 3, 9)
9
Plot the points in the table.
8
( 2, 7)
The points lie on a line. Find the slope by using the
7
6
points (− 2, 7) and (− 3, 9).
( 1, 5)
5
9 − 7
change in y
2
m =
=
=
= −2
—
—
—
(0, 3)
− 3 − (− 2)
− 1
change in x
2
Because the line crosses the y-axis at (0, 3), the y-intercept is 3.
1
So, the linear function is y = −2x + 3.
6
5
4
3
2
1
1
x
Use the graph or table to write a linear function that relates y to x.
Exercises 5–10
1.
2.
y
−2
−1
x
0
1
3
2
y
2
2
2
2
1
4
3
2
1
1
2
x
1
2
3
258
Chapter 6
Functions
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