© Edgenuity, Inc. 1

Warm-Up Using Equations to Represent Trend Lines

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WK2

Lesson Question

Words to Know

Fill in this table as you work through the lesson. You may also use the glossary to help you

correlation the description of the relation shared between sets of data

slope

the ratio of the change in the dependent values (outputs)

to the change in the values (inputs)

between two points on a line

slope-intercept form

the form of a linear relation that is written as is y = mx + b,

where m and b are numbers, m is the slope and

b is the y-intercept of the line

trend line a line that overlays a graph, showing

the average trend for all data points

Lesson Goals

Examine the

of a scatterplot.

line Write the equationof the trend line.

Find the

and

the y-intercept ofthe trend line.

© Edgenuity, Inc. 2

Instruction

2Slide

Using Equations to Represent Trend Lines

Finding the Slope of a Trend Line Using Data Points

EXAMPLE

When Bella started running, she kept a scatterplot of how many sunny days there were each month and how many miles she ran each month. The trend line Bella drew goes through points (15, 53) and (22, 66).

Use these points to determine how many extra miles Bella ran for every extra sunny day.

(x1, y1) = (15, 53)(x2, y2) = (22, 66)

Use the slope formula:

=−−

2 1

2 1

my y

x x

−

−=

53

22

m

= 13

7m

m ≈

For every extra sunny day, Bella will get an extra 1.9 of running in.

Bella’s Running Diary

x

y

Mile

s R

un

Number of Sunny Days

40

45

50

5560

65

70

10 15 20 25

© Edgenuity, Inc. 3

Instruction Using Equations to Represent Trend Lines

4Slide

Finding the Slope of a Trend Line without Data Points

Bella’s sister Betty also keeps notes on her running. She records how many miles she runs and how many ounces of water she drinks during the run.

How does the length of the run affect how much water she drinks?

(x1, y1) = (6, 13)(x2, y2) = (10, 22)

Use the slope formula:

=−−

2 1

2 1

my y

x x

−

−=

13

10

m

= 9

4m

m = ounces

For every extra that Betty runs, she drinks an extra 2.25 ounces of water.

Betty’s Running Diary

Miles Run

Wat

er (

oz)

x

y

2 4 6 8 10 12

5

10

15(6, 13)

(10, 22)

20

25

© Edgenuity, Inc. 4

Instruction Using Equations to Represent Trend Lines

6Slide

Writing the Equation for a Trend Line without the y-Intercept

EXAMPLE

Bella’s running data resulted in a positive correlation and a trend line with a slope of 1.9. Use the point (15, 53) of the data to write the equation of the line.

Bella’s Running Diary

x

y

Mile

s R

un

Number of Sunny Days

40

45

50

55

60

65

70

10 15 20 25

Slope-intercept form: y = mx +

53 = 1.9(15) + b

53 = + b53 − 28.5 = 28.5 − 28.5 + b

24.5 = b

Equation of the line:

y = 1.9x +

© Edgenuity, Inc. 5

Instruction Using Equations to Represent Trend Lines

9Slide

How to Find the Equation of a Trend Line

PROCEDURE

Data given as a set of points:

1. Make a scatterplot of the data.

2. Draw the trend line.

3. Find coordinate points on the trend line.

4. Write the equation of the line in form.

Creating a Scatterplot

Data for seven years of a quarterback’s passing statistics are shown by ordered pairs, where x is the number of passing attempts and y is the number of interceptions.

(150, 4), (252, 5), (254, 8), (296, 9), (312, 6), (440, 10), (446, 12).

Step 1. Make a scatterplot.

Step 2. Draw the trend line.

Pass Attempts

x

y

100 200 300 400 500

2

4

6

8

10

12Passing Data

Inte

rcep

tions

Draw a trend line.

© Edgenuity, Inc. 6

Instruction Using Equations to Represent Trend Lines

11Slide

Finding the Equation of a Trend Line

Pass Attempts

x

y

100 200 300 400

(400, 10)

(150, 4)

500

2

4

6

8

10

12

Passing DataIn

terc

eptio

ns

Find two points:

(x1, y1) = (150, 4)(x2, y2) = (400, 10)

Use the slope formula:

−−

=

=

10

400 150

6

250

m

m

m =

Find the y-intercept:

y = mx + b10 = 0.024(400) + b

10 = + b10 − 9.6 = 9.6 − 9.6 + b

= b

Write the equation in slope-intercept form:

y = + 0.4

© Edgenuity, Inc. 7

Summary Using Equations to Represent Trend Lines

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Answer

Use this space to write any questions or thoughts about this lesson.

Lesson Question How do you write the equation for a trend line?