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 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

(+,-)

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

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

Table Graph

(1,2)(2,4)(3,0)(4,5)

X 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.

Point 1= Point 1= (5, 10)(5, 10)

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”

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”

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”

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 PracticePositive, 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