Transcript Lesson 1-6 and 1-7

Lesson 1-6 and 1-7
Ordered Pairs and Scatter Plots
I Can…
 Use ordered pairs to locate points.
 Use tables and graphs to represent
relations.
 Construct scatter plots
 Interpret scatter plots
Ordered Pairs (Coordinate System)
 In mathematics, a
COORDINATE SYSTEM
is used to locate points.
 The coordinate system
is formed by the
intersection of two
number lines that meet
at right angles at their
zero points.
Coordinate System
The vertical
number line
is called the
Y-AXIS
Y
Quadrant
II
(-,+)
The ORIGIN is at
(0,0) the point at
which the
number lines
intersect.
Quadrant I
(+,+)
The coordinate
system is also
called the
COORDINATE
PLANE
X
Quadrant III
Quadrant IV
(-,-)
(+,-)
The
horizontal
number line
is called the
X-AXIS
Ordered Pair
 An ordered pair of numbers is used to locate any point
on a coordinate plane.
 The first number is called the x-coordinate.
 The second number is called the y-coordinate.
The x-coordinate
corresponds to a
number on the
X-AXIS
(3,2)
The y-coordinate
corresponds to a
number on the
Y-AXIS
Ordered Pairs
 To graph an ordered pair, draw a dot at the
point that corresponds to the ordered pair. The
coordinates are your directions to locate the
point.
Example 1: Graph Ordered Pairs
(2,3)
Step 1 Start at the origin
Step 2 Since the x-coordinate is
2, move 2 units to the
right.
Step 3 Since the y-coordinate is
3, move 3 units up. Draw a
dot.
M
Example 2: Identify Ordered Pairs
Write the ordered pair that names the point M.
Step 1 Start at the origin
Step 2 Move right on the x-axis
to find the x-coordinate
of point M, which is 3.
Step 3 Move up the y-axis to
find the y-coordinate,
which is 2
M
Relations
 A set of ordered pairs such as {(1,2), (2,4), (3,0), (4,5)} is a
relation.
 The DOMAIN of the relation is the set of x-coordinates.
 The RANGE of the relation is the set of y-coordinates.
{(1,2), (2,4), (3,0), (4,5)}
Relations
 A relation can be shown in several ways.
Ordered Pairs
(1,2)
(2,4)
(3,0)
(4,5)
Table
X
Graph
Y
Scatter Plots
 A scatter plot is a graph that shows the
relationship between two sets of data.
 In a scatter plot two sets of data are graphed as
ordered pairs on a coordinate system.
Why do we use scatterplots?
 Scatterplots allows us to SEE the relationship
between two sets of data.
Relationship between # of Disconnectin'
Phone Calls and Rihanna's Disturbia
# of Disconnectin' Calls
Point 1=
(5, 10)
200
150
100
50
0
0
20
40
60
% Disturbed
80
100
120
Scatterplot and Relationships
Scatterplots can show us three types of relationships
between our variables
1.
“think up”
POSITIVE
“think down”
2.
NEGATIVE
3.
NO RELATIONSHIP
??
Positive Relationships
 Shows a shape going
UP the graph.
 The plots are going up
the graph, showing us
that when one
variable increases, the
other does also.
“As Variable 1 increases, Variable 2
increases”
Negative Relationships
 Shows a shape going
DOWN the graph.
 The plots are going
down the graph,
showing us that as one
variable on the x-axis
increases, the variable
on the y-axis decreases.
“As Variable 1 increases, Variable 2
decreases”
No Relationship
??
 The plots are scattered all over the graph,
showing us that there is no obvious pattern or
relationship between the two variables.
Scatterplot Practice
Positive, Negative, or No Relationship
Predict…
Age of car and value of car
Predict…
Birth month and birth weight
Predict…
Hours of studying and test scores
on Friday’s test