Entry Task

Write the equation in slope intercept form and find the x and y intercepts.

1. 4x + 6y = 12

Chapter 2.5: Using Linear Chapter 2.5: Using Linear ModelsModels

Target: I can write linear equations that model real world data and make predictions from linear models.

Scatter PlotScatter Plot• A scatter plot is a graph of a collection of

ordered pairs (x,y).

• The graph looks like a bunch of dots, but some of the graphs are a general shape or move in a general direction.

Positive CorrelationPositive Correlation• If the x-coordinates and the

y-coordinates both increase, then it is POSITIVE CORRELATION.

• This means that both are going up, and they are related.

Positive CorrelationPositive Correlation• If you look at the age of a child and the

child’s height, you will find that as the child gets older, the child gets taller. Because both are going up, it is positive correlation.

Age 1 2 3 4 5 6 7 8Height “ 25 31 34 36 40 41 47 55

Negative CorrelationNegative Correlation• If the x-coordinates and the y-

coordinates have one increasing and one decreasing, then it is NEGATIVE CORRELATION.

• This means that 1 is going up and 1 is going down, making a downhill graph. This means the two are related as opposites.

Negative CorrelationNegative Correlation• If you look at the age of your family’s car and

its value, you will find as the car gets older, the car is worth less. This is negative correlation.

Age of car

1 2 3 4 5

Value $30,000 $27,000 $23,500 $18,700 $15,350

No CorrelationNo Correlation• If there seems to be

no pattern, and the points looked scattered, then it is no correlation.

• This means the two are not related.

No CorrelationNo Correlation• If you look at the size

shoe a baseball player wears, and their batting average, you will find that the shoe size does not make the player better or worse, then are not related.

ScatterplotsWhich scatterplots below show a linear trend?

a) c) e)

b) d) f)

NegativeCorrelation

PositiveCorrelation

ConstantCorrelation

Year

Sport Utility Vehicles(SUVs) Sales in U.S.

Sales (in Millions) 199119921993199419951996199719981999

0.91.11.41.61.72.12.42.73.2

1991 1993 1995 1997 1999 1992 1994 1996 1998 2000

x

y

Year

Veh

icle

Sal

es (M

illio

ns)

5

4

3

2

1

Objective - To plot data points in the coordinate plane and interpret scatter plots.

1991 1993 1995 1997 1999 1992 1994 1996 1998 2000

x

y

Year

Veh

icle

Sal

es (M

illio

ns)

5

4

3

2

1

Trend is increasing.

Scatterplot - a coordinate graph of data points.

Trend appears linear.

Positive correlation.

Year SUV Sales

Predict the sales in 2001.

1991 1993 1995 1997 1999 1992 1994 1996 1998 2000

x

y

Year

Veh

icle

Sal

es (M

illio

ns)

5

4

3

2

1

Scatterplot - a coordinate graph of data points.

Write the equation of the trend line.

Step 1 choose 2 points on the trend line. (1992, 1.1) and (1997, 2.4)

Step 2 write an equation in slope intercept form

Step 3 use the equation to predict the trend for 2001.

Plot the data on the graph such that homework timeis on the y-axis and TV time is on the x-axis..

StudentTime SpentWatching TV

Time Spenton Homework

Sam

Jon

Lara

Darren

Megan

Pia

Crystal

30 min.

45 min.

120 min.

240 min.

90 min.

150 min.

180 min.

180 min.

150 min.

90 min.

30 min.

90 min.

90 min.

90 min.

Plot the data on the graph such that homework timeis on the y-axis and TV time is on the x-axis.

TV Homework

30 min.

45 min.

120 min.

240 min.

90 min.

150 min.

180 min.

180 min.

150 min.

90 min.

30 min.

120 min.

120 min.

90 min.

Time Watching TV

Tim

e on

Hom

ewor

k

30 90 150 210 60 120 180 240

240210180150120 90 60 30

Describe the relationship between time spent onhomework and time spent watching TV.

Time Watching TV

Tim

e on

Hom

ewor

k

30 90 150 210 60 120 180 240

240210180150120 90 60 30

Trend is decreasing.

Trend appears linear.

Negative correlation.

Time on TV Time on HW

Let’s do it with a Calculator!

Make a scatterplot, draw the trend line and write the equation of the trend line.

Directions are on page 95 but watch here first

(2,58),(6,105),(8,88),(8,118),(12,117),(16,137),(20,157),(20,169)

1. Enter the Data into Lists• Press STAT. • Under EDIT, select 1: Edit. • Enter x-values (input) into L1 • Enter y-values (output) into L2.• After data is entered in the lists, go

to 2nd MODE to quit and return to the home screen.

• Note: If you need to clear out a list, for example list 1, place the cursor on L1  then hit CLEAR and ENTER .

2. Set up the Scatterplot.

• Press 2nd Y= (STAT PLOTS).• Select 1: PLOT 1 and hit ENTER. • Use the arrow keys to move the cursor

down to On and hit ENTER.• Arrow down to Type: and select the first

graph under Type.• Under Xlist: Enter L1.• Under Ylist: Enter L2.• Under Mark: select any of these.

3. View the Scatterplot

• Press 2nd MODE to quit and return to the home screen.

• To plot the points, press ZOOM and select 9: ZoomStat.

• The scatterplot will then be graphed.

4. Find the regression line.• Press STAT.• Press CALC.• Select 4: LinReg(ax + b). • Press 2nd 1 (for List 1)• Press the comma key,• Press 2nd 2 (for List 2) • Press ENTER.  

5. Interpreting and Visualizing

• Interpreting the result: y = ax + b

– The value of a is the slope – The value of b is the y-intercept– r is the correlation coefficient– r2 is the coefficient of determination

5. Interpreting and Visualizing

• Write down the equation of the line in slope intercept form.

• Press Y= and enter the equation under Y1. (Clear all other equations.) 

• Press GRAPH and the line will be graphed through the data points.

Homework

Homework – p. 96 #7,8,11,12,13,14,15,16,18,20

Challenge - # 19