11/23/2010 Evergreen Public Schools 2010 1 Lines to Model Data Teacher Notes Use point-slope formula...

11/23/2010©Evergreen Public Schools

20101

Lines to Model DataTeacher Notes

Use point-slope formula to write equations of lines that model linear data.

y – y1 = m(x – x1)We felt it was necessary to introduce point-slope form when

making estimations (prediction) and using decimal slopes.

Identify 2 points on the linear model. The points used to write the equation of the line are not usually data points.

Supplies: Copies of the Olympic Medals data for slide 19.

©Evergreen Public Schools 2010

2

Linear Models Target 3bI can write the equation of a line that is

a good model for the data.

What do you already know that might be used in this

lesson?


3

LaunchWrite the equation of the line.

(3, 500)

(8, 2300)


4


5

Lines to Model DataLines to Model Data


6

Lines to Model DataLines to Model DataWe have used computer software to draw

the best line that models the data.


7

Find two points on the lineFind two points on the line

(4, 5)

(8.5, 15)

Notice, there are no data

points on the line.


8

Find two points on the lineWe want the equation of the line that

passes through the points.

(4, 5)

(8.5, 15)


9

Lines to Model DataLines to Model DataWe want the equation of the line that

passes through the points (4, 5) and (8.5, 15).Find the slope.Leave it mixed with fractions &

decimals.

Did you get ?

104.5


10

Lines to Model DataLines to Model DataWe want the equation of the line that

passes through the points (4, 5) and (8.5, 15).

The slope is

Find the equation.I’ll get you started.

The equation is

104.5

104.5

y 5x 4

y104.5x

17.54.5


11

Lines to Model DataLines to Model DataOk. This equation is ugly!!

Let’s not mix the fractions & decimals.Change it to decimal approximations.Go to the tenths place.

y = 2.2x – 3.9

y104.5x

17.54.5


12

Lines to Model DataLines to Model DataWhat if we started with the slope in decimal

form?

What’s next?Eliminate the denominator.

104.5

y 5x 4

2.2y 5x 4

2.2y 5x 4

(x – 4) (x –

4)

2.2(x 4)y 5


13

Lines to Model DataLines to Model DataLet’s rewrite in slope-intercept form.

2.2(x – 4) = y – 5

y – 5 = 2.2(x – 4)y – 5 = 2.2x – 8.8

y = 2.2x – 3.8


14

Lines to Model DataLines to Model DataThe first equation was y = 2.2x – 3.9.

The second equation, when using a decimal slope was y = 2.2x – 3.8.

Are these close enough?


15

Lines to Model DataLines to Model Data


16

Point-Slope Formy – 5 = 2.2(x – 4)

m = 2.2

point is (4, 5)

y – y1 = m(x – x1)


17

Point-Slope FormUse y – y1 = m(x – x1) to find the equation of the linear model.


18

We now have 3 formulas to write equations of lines.

y – y1 = m(x – x1)

y = mx + b m

y2−y

1

x2−x

1


19

DebriefWhy might it be helpful to

have three different ways to write the equation for a line?


20

5

3

12

4

Did you hit the target? I can write an equation of

a line that is a good model for a set of data.

Rate your understanding of the target from 1 to 5.5 is a bullseye!


21

Ticket Out Write the

equation of the linear model.

11/23/2010 Evergreen Public Schools 2010 1 Lines to Model Data Teacher Notes Use point-slope formula...

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