FINDING THE EQUATION OF A TREND LINE WORKSHEET

Problem 1 :

Lily is getting trained for a 10K race. For some of her training runs, she records the distance she ran and how many minutes she ran.

Distance (miles)

4

2

1

2

3

5

2

4

3

Time (minutes)

38

25

07

16

26

55

20

45

31

Draw a trend line that shows the relationship between distance and time. And also write an equation for the trend line.

Problem 2 :

David records the number of chapters and the total number of pages for several books as given below. 

No. of Chapters

3

4

5

8

10

11

15

17

19

No. of Pages

20

44

50

95

90

130

125

170

160

Draw a trend line that shows the relationship between the number of chapters and the number of pages. And also write an equation for the trend line.

Answers

1. Answer :

Distance (miles)

4

2

1

2

3

5

2

4

3

Time (minutes)

38

25

07

16

26

55

20

45

31

Step 1 :

Make a scatter plot of Lily’s running data.

Step 2 :

To draw a trend line, use a straight edge to draw a line that has about the same number of points above and below it. Ignore any outliers.

Step 3 : 

Find the slope of the trend line.

The line passes through points (2, 20) and (4.5, 45).

Use the slope formula. 

m  =  (y2y1)/(x2x1)

Substitute x1, = 2, y1 = 20, x2 = 4,  and y2 = 45.

m  =  (45 - 20)/(4.5 - 2)

m  =  25/2.5

m  =  10

Step 4 : 

Find the y-intercept of the trend line.

Slope-intercept form equation of a line : 

y  =  mx + b

Plug y = 20, m = 10 and x = 2. 

20  =  10 · 2 + b

20  =  20 + b

Subtract 20 from both sides. 

0  =  b

Step 5 : 

Use your slope and y-intercept values to write the equation.

Slope-intercept form equation of a line : 

y  =  10x + 0

So, the equation for the trend line is

y  =  10x

2. Answer :

No. of chapters

3

4

5

8

10

11

15

17

19

No. of pages

20

44

50

95

90

130

125

170

160

Step 1 :

Make a scatter plot of the data given above. 

Step 2 :

To draw a trend line, use a straight edge to draw a line that has about the same number of points above and below it. Ignore any outliers.

Step 3 : 

Find the slope of the trend line. The line passes through points (5, 50) and (17, 170).

Use the slope formula. 

m  =  (y2 - y1)/(x2 - x1)

Substitute x1, = 5, y1 = 50, x2 = 17,  and y2 = 170.

m  =  (170 - 50)/(17 - 5)

m  =  120/12

m  =  10

Step 4 : 

Find the y-intercept of the trend line.

Slope-intercept form equation of a line : 

y  =  mx + b

Plug y = 50, m = 10 and x = 5. 

50  =  10 · 5 + b

50  =  50 + b

Subtract 50 from both sides. 

0  =  b

Step 5 : 

Use your slope and y-intercept values to write the equation.

Slope-intercept form equation of a line : 

y  =  mx + b

y  =  10x + 0

So, the equation for the trend line is

y  =  10x

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