**Finding the equation of a trend line worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on scatter plots and equations of trend lines.

**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.

**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.

**Solution : **

**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 = (y₂ - y₁) / (x₂ - x₁)

Plug 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

The equation for the trend line is y = 10x.

**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.

**Solution :**

**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)

Plug 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

The equation for the trend line is y = 10x.

After having gone through the stuff given above, we hope that the students would have understood, "Finding the equation of a trend line worksheet".

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