Download Document

Graphing Equations
and Inequalities
Survey A
Complete each ordered pair.
1. 
( 3, __ ) if 2x – 8y = -2
(3 , 1)
2. 
( __ , -2 ) if y = x +7
(-24, -2)
3. 
( -4 , __ ) if y = -3x – 5
(-4 , 7)
4. 
( __ , -½ ) if 3x – 6y = -1 (-4/3 , -1/2)
Survey A
2
Graphing Linear
Equations
Survey A
  Graph
a linear equation by
finding and plotting ordered
pair solutions
Survey A
4
Linear Equation in Two Variables
A linear equation in two variables is an equation
that can be written in the form
Ax + By = C
where A, B, and C are real numbers and A and B are
not both 0.
 This form is called standard form.
 The graph of a linear equation in two variables is a
straight line.
Survey A
5
Example 1
Graph the linear equation 2x – y = -4
To graph this equation, we find three ordered
pair solutions by choosing a value for one of the
variables, x or y, then solving for the other
variable.
(The third solution acts as a check for the other two.)
We will plot the solution points, then draw the
line containing the 3 points.
Survey A
6
Graph the linear equation 2x – y = – 4.
Let x = 1. 2x – y = –4
2(1) – y = –4
2 – y = –4
– y = –6
y=6
Replace x with 1.
Simplify.
Subtract 2 from both sides.
Multiply both sides by –1.
The ordered pair (1, 6) is a solution of 2x – y = – 4.
Survey A
7
Graph the linear equation 2x – y = – 4.
Next, let y = 4. 2x – y = –4
2x – 4 = –4
2x = – 4 + 4
2x = 0
x=0
Replace y with 4.
Add 4 to both sides.
Simplify.
Divide both sides by 2.
The ordered pair (0, 4) is a second solution.
Survey A
8
Graph the linear equation 2x – y = – 4.
Next, let x = -3.
2x – y = –4
2(-3) – y = –4
– 6 – y = –4
–y = 2
y = –2
Replace x with –3.
Simplify.
Add 6 to both sides.
Multiply both sides by –1.
The third solution is (–3, –2).
Survey A
9
y
(1, 6)
Now we plot all three of
the solutions (1, 6), (0, 4)
and (–3, –2).
Then, we draw the
line that contains
the three points.
Survey A
(0, 4)
x
(– 3, – 2)
10
Example 2
Graph the linear equation y = ¾x + 3.
Since the equation is solved for y, we should
choose values for x.
To avoid fractions, we should select values of x
that are multiples of 4 (the denominator of the
fraction).
Survey A
11
Graph the linear equation y =
x + 3.
Let x = 4. y = x + 3
y=
(4) + 3
y=3+3=6
Replace x with 4.
Simplify.
So one solution is (4, 6).
Survey A
12
Graph the linear equation y =
x + 3.
Next, let x = 0. y=
y=
x + 3
(0) + 3
y=0+3=3
Replace x with 0.
Simplify.
So a second solution is (0, 3).
Survey A
13
Graph the linear equation y =
x + 3.
Next, let x = –4. y=
x + 3
y=
(–4) + 3
y = –3 + 3 = 0
Replace x with – 4.
Simplify.
So the third solution is (–4, 0).
Survey A
14
y
Now we plot all three
of the ordered pair
solutions; (4, 6), (0, 3)
and (–4, 0).
Then, we draw
the line that
contains the
three points.
Survey A
(4, 6)
(0, 3)
x
(–4, 0)
15
When graphing a linear equation in
two variables, if it is:
•  solved for y, it may be easier to
find ordered pair solutions by
choosing x-values. If it is
•  solved for x, it may be easier to
find ordered pair solutions by
choosing y-values.
Survey A
16
Example 3
Graph the linear equation y = 3
Can be written in standard form as 0x + y = 3.
No matter what value we replace x with, y is always 3.
x
0
1
5
Survey A
y
3
3
3
17
1. Plot the points
2. Connect with
line
What kind of line
is this?
a horizontal line
** always y = # **
Survey A
18
Example 4
Graph the linear equation x = -2
Can be written in standard form as x + 0y = -2.
No matter what value we replace y with, x is always -2.
x
-2
-2
-2
Survey A
y
-2
0
1
19
1. Plot the points
2. Connect with
line
What kind of line
is this?
a vertical line
** always x = # **
Survey A
20
What three things do I need to
do in order to graph a linear
equation?
1.  Pick values to plug in to have
ordered pairs
2.  Plot the ordered pairs
3.  Connect with a line
Survey A
21