Algebra 1

Ch 4.1 Coordinates & Scatter Plots

Objective

Students will plot points on a coordinate plane

Students will draw scatter plots and make predictions

Before we begin…

Generally speaking, Algebra 1 is the in-depth study of linear equations…

For the next couple of chapters we will spend time looking at various aspects of linear equations…with the ultimate goal of making meaning out of the data…

To work with linear equations we must start at the beginning, which is working with the coordinate plane…

Coordinate Plane

The coordinate plane is formed by two real number lines that intersect at a right angle.The horizontal number line is called the x-axisThe vertical number line is called the y-axisThe plural of axis is called axes

The point at which the 2 number lines intersect is called the origin, which is identified with the ordered pair (0,0)

Coordinate Plane

x

yVertical Axis - Y

Horizontal Axis - X

Origin (0,0)

The Coordinate System

Each point in the plane corresponds to an ordered pair of real numbers

In an ordered pair the x-coordinate is always displayed first, then the y-coordinate

Example: (3, 4)

This is the x-coordinate

This is the y-coordinate

The Coordinate Plane

To plot an ordered pair on the coordinate plane:Move horizontally along the x-axis and locate

the x value. Then move vertically to locate the y value.The point at which they meet is the ordered

pair.

Let’s look at an example…

Example 1Plot the ordered pair (3, 4)

In this example 3 is the x value so starting at 0 move 3 spaces to the right on the x-axis

4 is the y value so move 4 spaces up on the y-axis to find the ordered pair

x

y

(3,4)

Example 2Plot the ordered pair (-3, -4)

In this example - 3 is the x value so starting at 0 move 3 spaces to the left on the x-axis

-4 is the y value so move 4 spaces down on the y-axis to find the ordered pair

x

y

(-3,-4)

The Coordinate Plane

The coordinate plane is comprised of four quadrants which are labeled counter-clockwise, using Roman Numerals, starting in the upper right hand corner.

y

x

Quadrant I

Quadrant IVQuadrant III

Quadrant II

The Coordinate Plane

In each quadrant the x and y values can be positive or negative as follows:

y

x

x = positive

y = positive

x = positive

y = negative

x = negative

y = negative

x = negative

y = positive

Scatter PlotsA scatter plot is a graph that shows the

relationship of two sets of data, which can be graphed as an ordered pair…

Scatter plots are used to see trends in data and to make predictions about the future…

A real-life example of a scatter plot is when your parents bring you to the doctor’s for check-ups….the doctor keeps statistics on your height and weight…and uses the information to determine if you are growing and maintaining weight at an appropriate level based upon your age…

Interpreting Scatter Plots

A scatter plot can show three types of relationships…No RelationshipNegative RelationshipPositive Relationship

After plotting the data you can look at the graph to determine the type of relationship…as shown on the next slide

Types of relationships

No Relationship Negative Relationship Positive Relationship

Types of Relationships

As illustrated in the previous slide:In a no relationship scatter plot the data points

appear to be random and have no direction

In a negative relationship the data points appear to be going in a downward direction

In a positive relationship the data points appear to be going in an upward direction

Example #3

Draw a scatter plot of the given data

TV Size 19 in 27 in 32 in 36 in

Price $179 $349 $499 $659

In this example the data above becomes the ordered pairs, with the TV size being the x-value and the price begin the y-value.

The data is plotted on the next slide…

TV Size 19 in 27 in 32 in 36 in

Price $179 $349 $499 $659

TV Size (in)

Pric

e ($

)

15 25 35 45 55

100

200

300

400

500

600

700

0

(19, 179)

(27, 349)

(32, 499)

(36, 659)

Interpreting the Data

After plotting the data in the scatter plot we can see that a relationship has formed between the size of the TV and the price of the TV.

In this example the data is going in an upward direction meaning that there is a positive relationship…

From the data and the relationship illustrated in the scatter plot we can make the statement “The larger the size of the TV the more it will cost.”

We can also predict that a 40 inch TV will cost between $700 and $800.

Comments

On the next couple of slides are some practice problems…The answers are on the last slide…

Do the practice and then check your answers…If you do not get the same answer you must question what you did…go back and problem solve to find the error…

If you cannot find the error bring your work to me and I will help…

Your Turn

Draw and label a coordinate plane. Plot and label the ordered pairs. (Use a separate Coordinate Plane for each set of points)

1. A(0,3), B(-2,-1), C(2,0)

2. A(0,0), B(2,-2), C(-2,0)

3. A(3,-5), B(1.5, 3), C(-3,-1)

Your Turn Without plotting the point identify the Quadrant:4. (5,-3)5. (6,17)6. (-5,-2)7. (-5,6)Make a scatter plot of the data

Time 1:00 3:00 5:00 7:00

Temp. 71° 74° 68° 63°

8. Identify the relationship as positive, negative, or no relationship

9. What statement can you make about the relationship of time and temperature?

10. Predict what the temperature will be at 9:00

Summary

A key tool in making learning effective is being able to summarize what you learned in a lesson in your own words…

In this lesson we talked about The Coordinate Plane and Scatter Plots Therefore, in your own words summarize this lesson…be sure to include key concepts that the lesson covered as well as any points that are still not clear to you…

I will give you credit for doing this lesson…please see the next slide…

Credit

I will add 25 points as an assignment grade for you working on this lesson…

To receive the full 25 points you must do the following: Have your name, date and period as well a lesson number as

a heading. Do each of the your turn problems showing all work Have a 1 paragraph summary of the lesson in your own words

Please be advised – I will not give any credit for work submitted: Without a complete heading Without showing work for the your turn problems Without a summary in your own words…