When a linear association is shown by a scatter plot, we can use a line to model the relationship between the variables. A trend line is a straight line that comes closest to the points on a scatter plot. We can use two points on a trend line to write an equation in slope-intercept form for the trend line.

**Example 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 = (y_{2} - y_{1}) / (x_{2} - x_{1})

Substitute x_{1}, = 2, y_{1} = 20, x_{2} = 4, and y_{2} = 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

**Example 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 = (y_{2} - y_{1}) / (x_{2} - x_{1})

Substitute x_{1}, = 5, y_{1} = 50, x_{2} = 17, and y_{2} = 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

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**