Studying Scatter Plots

Create a graph of this data

Create a graph of this data

Create a graph of this data

Do all three graphs show the same type of growth?

What kind of growth is shown by each

Negative Correlation

Positive Correlation

No Correlation

Draw a line that represents how the data is changing.

Use the line to predict what number matches up with x = 8.

Use the line to predict what number matches up with y = 6.

Draw a line that represents how the data is changing.

Use the line to predict the value that matches up with x = 4.

Use the line to predict the value that matches up with y = 2.

Is there a line that represents how this data is changing?

We say that this line has no correlation.

Writing Equations to Represent Data

• When lines have positive or negative correlation you can write equations to represent the data.

After the line is drawn, select two points on the line and draw the right triangle that shows its rise and run

Write a fraction for the steepness of the line.

51

5m

Find the y-intercept. 0b Write the equation in slope intercept form.

1 0

1

y x

y x

If x = 9, what does y equal?

1

1(9)

9

y x

y

y

After the line is drawn, select two points on the line and draw the right triangle that shows its rise and run

Write a fraction for the steepness of the line.

3 16 2

m

Find the y-intercept.

5b

Write the equation in slope- intercept form.

15

2y x

Predict the y value that matches with x = 4

15

21

4 52

3

y x

y

y

Real-World Problem

Pedaling time (min)

0 1 2 20 30 45 60

Total Calories burned

215 220 225 300 335 405 460

Allison runs to the gym from home and burns 215 calories during the run. Then over the next hour (60 minutes) she continues to burn calories at the gym by using the various equipment. The calories she burned, while at the gym are recorded in the chart.

• Create a scatter plot of the pedaling time vs. total calories burned.• Draw a line of best fit for the data.• Write an equation for your line of best fit.• Use your line to predict how many calories she would burn in 25

minutes. • Use your line to predict how long she had to work at the gym to

burn 250 calories.

Pedaling time (min)

0 1 2 20 30 45 60

Total Calories burned

215 220 225 300 335 405 460

min

calo

ries

Time pedaling vs. Total Calories Burned

200

300

400

500

600

60

30

45

153 6 9 12

460-215or245

60-0 or 60

2454

60m 215b

4 215y x

Pedaling time (min)

0 1 2 20 30 45 60

Total Calories burned

215 220 225 300 335 405 460

min

calo

ries

Time pedaling vs. Total Calories Burned

200

300

400

500

600

60

30

45

153 6 9 12

4 215y x • Use your line to predict how many calories she would burn in 25 minutes.

When x = 25, y=4(25)+215 =315 calories

Pedaling time (min)

0 1 2 20 30 45 60

Total Calories burned

215 220 225 300 335 405 460

min

calo

ries

Time pedaling vs. Total Calories Burned

200

300

400

500

600

60

30

45

153 6 9 12

4 215y x • Use your line to predict how long she had to work at the gym to burn 250 calories.

When y=250, 250=4x+215 35=4xX≈9 minutes

Studying Scatter Plots