lesson 1-6 and 1-7 ordered pairs and scatter plots
TRANSCRIPT
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Lesson 1-6 and 1-7 Ordered Pairs and Scatter Plots
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I Can…
Use ordered pairs to locate points.
Use tables and graphs to represent relations.
Construct scatter plots
Interpret scatter plots
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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.
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Coordinate System
The horizontal number line is
called the X-axis
The coordinate
system is also called the
COORDINATE PLANE
The vertical number line is
called the Y-axis
The ORIGIN is at (0,0) the
point at which the number
lines intersect.
X
Y
Quadrant I
(+,+)
Quadrant II
(-,+)
Quadrant III
(-,-)
Quadrant IV
(+,-)
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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.
(3,2)
The y-coordinate corresponds to a number on the
Y-AXIS
The x-coordinate
corresponds to a number on
the
X-AXIS
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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.
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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
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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
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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)}
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Relations
A relation can be shown in several ways.
Ordered Pairs
Table Graph
(1,2)(2,4)(3,0)(4,5)
X Y
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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.
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Why do we use scatterplots?
Scatterplots allows us to SEE the relationship between two sets of data.
Point 1= Point 1= (5, 10)(5, 10)
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Scatterplot and Relationships
Scatterplots can show us three types of relationships between our variables
1. POSITIVE
2. NEGATIVE
3. NO RELATIONSHIP????
““think think up”up”
““think think down”down”
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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 As Variable 1 increases, Variable 2
increases”increases”
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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 As Variable 1 increases, Variable 2 decreases”decreases”
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No Relationship
The plots are scattered all over the graph, showing us that there is no obvious pattern or relationship between the two variables.
????
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Scatterplot PracticePositive, Negative, or No Relationship
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Predict…
Age of car and value of car
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Predict…
Birth month and birth weight
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Predict…
Hours of studying and test scores on Friday’s test