1. 11/23/2010 ©Evergreen Public Schools 2010 1 Lines to Model Data Teacher Notes Use point-slope formula to write equations of lines that model linear data. y – y 1 = m ( x – x 1 ) 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.

2. ©Evergreen Public Schools 2010 2 Learning Target Linear Models Target 3b I 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. ©Evergreen Public Schools 2010 3 Launch Write the equation of the line. (3, 500) (8, 2300)

4. ©Evergreen Public Schools 2010 4 ExploreExplore

5. 5 Lines to Model Data From yesterday

6. ©Evergreen Public Schools 2010 6 Lines to Model Data We have used computer software to draw the best line that models the data.

7. ©Evergreen Public Schools 2010 7 Find two points on the line (4, 5) (8.5, 15) Notice, there are no data points on the line.

8. ©Evergreen Public Schools 2010 8 Find two points on the line We want the equation of the line that passes through the points. (4, 5) (8.5, 15)

9. ©Evergreen Public Schools 2010 9 Lines to Model Data We 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 ?

10. ©Evergreen Public Schools 2010 10 Lines to Model Data We 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

11. ©Evergreen Public Schools 2010 11 Lines to Model Data Ok. This equation is ugly!! Let’s not mix the fractions & decimals. Change it to decimal approximations. Go to the tenths place. y = 2.2 x – 3.9

12. ©Evergreen Public Schools 2010 12 Lines to Model Data What if we started with the slope in decimal form? What’s next? Eliminate the denominator. (x – 4)

13. ©Evergreen Public Schools 2010 13 Lines to Model Data Let’s rewrite in slope-intercept form. 2.2( x – 4) = y – 5 y – 5 = 2.2( x – 4) y – 5 = 2.2 x – 8.8 y = 2.2 x – 3.8

14. ©Evergreen Public Schools 2010 14 Lines to Model Data The first equation was y = 2.2 x – 3.9. The second equation, when using a decimal slope was y = 2.2 x – 3.8. Are these close enough?

15. ©Evergreen Public Schools 2010 15 Lines to Model Data So now we have ( x – 4)2.2 = y – 5 Let’s rewrite 2.2( x – 4) = y – 5 y – 5 = 2.2( x – 4) y – 5 = 2.2 x – 8.8 y = 2.2 x – 3.8

16. ©Evergreen Public Schools 2010 16 Point-Slope Form y – 5 = 2.2( x – 4) m = 2.2 point is (4, 5) y – y 1 = m ( x – x 1 )

17. ©Evergreen Public Schools 2010 17 Point-Slope Form Use y – y 1 = m ( x – x 1 ) to find the equation of the linear model.

18. ©Evergreen Public Schools 2010 18 We now have 3 formulas to write equations of lines. y – y 1 = m ( x – x 1 ) y = mx + b

19. ©Evergreen Public Schools 2010 19 Debrief Why might it be helpful to have three different ways to write the equation for a line?

20. ©Evergreen Public Schools 2010 20 5 3 1 2 4 Learning Target 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. ©Evergreen Public Schools 2010 21 Ticket Out Write the equation of the linear model.