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)(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 1Start at the origin Step 2Since the x-coordinate is 2, move 2 units to the right. Step 3Since 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 1Start at the origin Step 2Move right on the x-axis to find the x-coordinate of point M, which is 3. Step 3Move 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 PairsTableGraph (1,2) (2,4) (3,0) (4,5) XY

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= (5, 10)

Scatterplot and Relationships Scatterplots can show us three types of relationships between our variables 1. POSITIVE 2. NEGATIVE 3. NO RELATIONSHIP ?? “think up” “think 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 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