Transcript Holt CA Course 1 2-8 - Jefferson School District

2-8 Graphing Equations
California
Standards
AF1.0 Students write verbal expressions and
sentences as algebraic expressions and
equations; they evaluate algebraic expressions,
solve simple linear equations, and graph and
interpret their results.
Also covered:
NS2.3
Holt CA Course 1
2-8 Graphing Equations
Vocabulary
linear equation
An equation whose solutions form a straight line on a
coordinate plane.
Holt CA Course 1
2-8 Graphing Equations
Example 1: Finding Solutions of Equations
with Two Variables
Use the given x-values to write solutions of
the equation as ordered pairs.
y = 4x + 2; x = 1, 2, 3, 4.
Make a table by using the
Write these
given values for x to find
solutions as
values for y.
ordered pairs.
x
4x + 2
y
(x, y)
1
4(1) + 2
6
(1, 6)
2
4(2) + 2
10
(2, 10)
3
4(3) + 2
14
(3, 14)
4
4(4) + 2
18
(4, 18)
Holt CA Course 1
2-8 Graphing Equations
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.
Holt CA Course 1
2-8 Graphing Equations
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.
Holt CA Course 1
2-8 Graphing Equations
You can also graph the solutions of an
equation on a coordinate plane. When
you graph the ordered pairs given by
some equations, they form a straight
line. For this reason, these equations
are called linear equations.
Holt CA Course 1
2-8 Graphing Equations
Example 3: Reading Solutions on Graphs
Use the graph of the linear equation 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
Move up until you
reach the graph. Move
left to find the y-value
on the y-axis.
-4
When x = 4, y = 2.
2
x
-4
-2
0
2
4
The ordered pair is (4, 2).
Holt CA Course 1
2-8 Graphing Equations
Example 4: Graphing Linear Functions
Graph the equation y = –x – 2.
Make a table. Substitute
different values for x.
Write the solutions as
ordered pairs.
x
–x – 2
y
(x, y)
–1
–(–1) – 2
–1
(–1, –1)
0
–(0) – 2
–2
(0, –2)
1
–(1) – 2
–3
(1, –3)
Holt CA Course 1
2-8 Graphing Equations
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
Holt CA Course 1
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.
2-8 Graphing Equations
Check It Out! Example 1
Use the given x-values to write solutions of
the equation as ordered pairs.
y = 3x + 2; x = 2, 3, 4, 5.
Make a function table by
using the given values for x
to find values for y.
Write these
solutions as
ordered pairs.
x
3x + 2
y
(x, y)
2
3(2) + 2
8
3
3(3) + 2
11
4
3(4) + 2
14
(2, 8)
(3, 11)
(4, 14)
5
3(5) + 2
17
(5, 17)
Holt CA Course 1
2-8 Graphing Equations
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, yes (4, 20) is a solution to y = 5x.
Holt CA Course 1
2-8 Graphing Equations
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).
Holt CA Course 1
2-8 Graphing Equations
Check It Out! Example 4
Graph the equation. y = –x – 4
Make a table. Substitute
different values for x.
Write the solutions as
ordered pairs.
x
–x – 4
y
(x, y)
–1
–(–1) – 4
–3
(–1, –3)
0
–(0) – 4
–4
(0, –4)
1
–(1) – 4
–5
(1, –5)
Holt CA Course 1
2-8 Graphing Equations
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
Holt CA Course 1
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.