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1.9 Patterns, Equations, and
Graphs
Review: Two number lines that intersect at a right angle form a
COORDINATE PLANE
The horizontal axis is called the x-AXIS
The vertical axis is called the y-AXIS
An ORDERED PAIR of numbers names the location of a point on the
plane.
These numbers are the COORDINATES of the point.
The first coordinate is the x-COORDINATE and the second is the
COORDINATE
The graph is split into 4 sections called: QUADRANTS
y-
The x-y Plane:
Mathematicians use a
horizontal and vertical
____________
to divide a
axes
plane into four regions called
______________.
quadrants
The horizontal line is
x
x- axis.
called the _____
The vertical line is called the
y- axis.
____
The x and y-axes intersect
origin
at the ___________.
y
The x-y Plane:
(6,5)
Any point on the coordinate
system is written as an
ordered pair
______________.
The coordinate of the
origin would be
(0,
0)
represented
by
________.
x
The first number in an
ordered pair is the
____________________.
x-coordinate
y
The second number in an
ordered pair is the
___________________
y- coordinate
Example 1 – Name the letter that corresponds to the following
points, and give its quadrant:
y
S
D
1) (1, 3): ______
C ______
I
B
C
V
2) (-4, 6): ______
______
B
II
E
x
F
3) (8, -2): ______
______
IV
O
F
A
H
N
4) (-9, -6): ______
______
A
III
Example 1 – Name the coordinates of the following points:
y
S
(0, 9)
5) N ______
D
B
(6, 4)
6) H ______
C
V
E
x
O
F
A
H
N
(8,3)
7) V ______
(2,8)
8) S ______
Using Integers to Graph Equations
Given a constant wind speed of 7 miles per hour, the
windchill temperature can be determined by subtracting 5
from the current temperature. Basically the following is the
equation for determining the windchill temperature given a
7 mph wind.
Actual
°F
5
Wind
Chill
Temperature - _______________
_______________ = ________________
or
w
a
5
_______________ = ______________ - ________________
Creating a table of values
We can use this equation to create a table of values by
substituting actual temperatures in for a to find
windchill temperatures w.
The two values, a and w, can be combined to form an
Ordered
Pair , (a, w)
Creating a table of values
Actual Temp
a
Windchill Temp.
w=a–5
-10
w  10  5  15
-5
w  5  5  10
0
w  0  5  5
5
w  55  0
10
w  10  5  5
15
w  15  5  10
20
w  20  5  15
Ordered Pair
(a, w)
 10, 15
 5, 10 
 0, 5
 5,0 
10,5
15,10 
 20,15
Graphing from a Table of Values
Now we can take the ordered pairs from above and graph them
on a coordinate plane.
The coordinate of the ORIGIN
represented by (0, 0)
.
would be
Horizontal
The first number in an ordered pair is the ______________
component.
Vertical
The second number in an ordered pair is the ____________
component.
w
First coordinates that are
negative go on the
Left
____________of
the origin.
First coordinates that are
positive go on the
Right
____________of
the origin.
Second coordinates that are
negative go ____________
Below the
origin.
Second coordinates that are
positive go ____________
Above the
origin.
a
Now, plot the points from the table above for (a, w).
20
 10, 15
 5, 10 
10
 0, 5
-20
20
-10
 5,0 
10,5
15,10 
 20,15
-20
If you connect the points,
20
what graph would you get?
A Line
_______________________
10
The equation w = a − 5 is
called a:
Equation -20
__________
Linear ____________
20
-10
A linear equation is an
equation whose graph is
A Line
__________________.
-20
Writing Linear Equations
Patterns in data can be described using linear equations.
The following table gives the cost y, in dollars for renting a raft
at the beach for a time x hours. Use the table to predict an
equation relating the data, and predict the cost to rent a raft for
8 hours.
Time (in hours), x
0
1
2
3
Cost (in dollars), y
10
15
20
25
y  10  5 x
Equation: _______________________
Meaning:
_______________________________________________
The cost of the raft rental is $10, plus $5 per hour
y  10  5(8)  50
Prediction for 8 hours:____________________________
The solution to an equation is the set of ordered pairs that
make an equation TRUE.
EXAMPLE: Determine whether the given equation has the
ordered pair as a solution.
1)
y  x  4;  5,1
1 54
11
2)
 1
y  x  ; 1, 
2  2
1
1
 1
2
1
2
TRUE
1
x
3)
3
 y; (2, 6)
1
2
2
3
 6
1
2
FALSE
FALSE
Homework :
Section 1.8 pages 64-66
#’s 8, 12, 13, 17, 22, 24, 26, 28, 31, 34, 38, 41, 43, 55-58