Transcript 10-2

10-2
Graphing Functions
Learn to represent linear functions using
ordered pairs and graphs.
10-2
Graphing Functions
Vocabulary
linear equation
10-2
Graphing Functions
Additional Example 1: Finding Solutions of
Equations with Two Variables
Use the given x-values to write solutions of
the equation y = 4x + 2 as ordered pairs. x =
1, 2, 3, 4.
Make a function table by
Write these
using the given values for x
solutions as
to find values for y.
ordered pairs.
x
1
2
3
4
4x + 2
4(1) + 2
4(2) + 2
4(3) + 2
4(4) + 2
y
6
10
14
18
(x, y)
(1, 6)
(2, 10)
(3, 14)
(4, 18)
10-2
Graphing Functions
Check It Out: Example 1
Use the given x-values to write solutions
of the equation y = 3x + 2 as ordered
pairs. x = 2, 3, 4, 5.
Make a function table by
using the given values for x
to find values for y.
x
2
3
4
5
3x + 2
3(2) + 2
3(3) + 2
3(4) + 2
3(5) + 2
y
8
11
14
17
Write these
solutions as
ordered pairs.
(x, y)
(2, 8)
(3, 11)
(4, 14)
(5, 17)
10-2
Graphing Functions
Check if an ordered pair is a solution of
an equation by putting the x and y
values into the equation to see if they
make it a true statement.
10-2
Graphing Functions
Additional Example 2: Checking Solutions of
Equations with Two Variables
Determine whether the ordered pair is a
solution to the given equation.
(3, 21); y = 7x
y = 7x
?
21 = 7(3)
Write the equation.
Substitute 3 for x and 21 for y.
?
21 = 21 
So (3, 21) is a solution to y = 7x.
10-2
Graphing Functions
Check It Out: Example 2
Determine whether the ordered pair is a
solution to the given equation.
(4, 20); y = 5x
y = 5x
Write the equation.
?
20 = 5(4)
?
20 = 20
Substitute 4 for x and 20 for y.

So (4, 20) is a solution to y = 5x.
10-2
Graphing Functions
You can also graph the solutions of an
equation on a coordinate plane. When
you graph the ordered pairs of some
functions, they form a straight line. The
equations that express these functions
are called linear equations.
Graphing Functions
10-2
Additional Example 3: Reading Solutions on
Graphs
Use the graph of the linear function to find
the value of y for the given value of x.
x=4
Start at the origin and
move 4 units right.
y
4
2
x
-4
-2
0
-2
-4
2
4
Move up until you
reach the graph. Move
left to find the y-value
on the y-axis.
When x = 4, y = 2.
The ordered pair is (4, 2).
Graphing Functions
10-2
Check It Out: Example 3
Use the graph of the linear function to find
the value of y for the given value of x.
x=2
Start at the origin and
move 2 units right.
y
4
2
x
-4
-2
0
-2
-4
2
4
Move up until you
reach the graph. Move
left to find the y-value
on the y-axis.
When x = 2, y = 4.
The ordered pair is (2, 4).
10-2
Graphing Functions
Additional Example 4: Graphing Linear
Functions
Graph the function described by the
equation. y = –x – 2
Make a function table.
Write these solutions as
ordered pairs.
(x, y)
(–1, –1)
x
–x – 2
y
–1
–(–1) – 2
–1
0
–(0) – 2
–2
(0, –2)
1
–(1) – 2
–3
(1, –3)
10-2
Graphing Functions
Additional Example 4 Continued
Graph the ordered pairs on a coordinate plane.
y
5
4
3
2
1
-5 -4 -3 -2 -1 0 1 2
-1
-2
-3
-4
-5
x
3 4 5
Draw a line through the
points to represent all the
values of x you could have
chosen and the
corresponding values of y.
10-2
Graphing Functions
Check It Out: Example 4
Graph the function described by the
equation. y = –x – 4
Make a function table.
Write these solutions as
ordered pairs.
(x, y)
(–1, –3)
x
–x – 4
y
–1
–(–1) – 4
–3
0
–(0) – 4
–4
(0, –4)
1
–(1) – 4
–5
(1, –5)
10-2
Graphing Functions
Check It Out: Example 4 Continued
Graph the ordered pairs on a coordinate plane.
y
5
4
3
2
1
-5 -4 -3 -2 -1 0 1 2
-1
-2
-3
-4
-5
x
3 4 5
Draw a line through the
points to represent all the
values of x you could have
chosen and the
corresponding values of y.