0021_A2_AIOsw07_DNG_ch02.qxd

04/18/07

12:09 pm

Page 30

Name_____________________________________ Class____________________________ Date________________

Lesson 2-4

Using Linear Models

Lesson Objectives 1 Modeling real-world data 2 Predicting with linear models

Vocabulary.

y

y

y

x

Weak

x

Strong

correlation

y

correlation

y

x

Weak correlation

All rights reserved.

A scatter plot is

Strong

x

x

correlation

correlation

Examples. 1 Transportation Suppose an airplane descends at a rate of 300 ft/min from an elevation of 8000 ft. Write and graph an equation to model the plane’s elevation as a function of the time it has been descending. Interpret the intercept at which the graph intersects the vertical axis.

d 8000 6000 4000 2000 t O

Relate

plane’s elevation



rate



time



10

20

30

starting elevation

Define Let t  time (in minutes) since the plane began its descent. Let d  the plane’s elevation. Write

d



300



An equation that models the plane’s elevation is

(

The d-intercept is 0, was 30



t





.

). This tells you that the elevation of the plane

ft at the moment it began its descent.

Algebra 2 Lesson 2-4

Daily Notetaking Guide

© Pearson Education, Inc., publishing as Pearson Prentice Hall.

A trend line is

0021_A2_AIOsw07_DNG_ch02.qxd

04/18/07

12:09 pm

Page 31

Name_____________________________________ Class____________________________ Date ________________

2 Using a Linear Model A spring has a length of 8 cm when a 20-g mass is hanging at the bottom end. Each additional gram stretches the spring another 0.15 cm. Write an equation for the length y of the spring as a function of the mass x of the attached weight. Step 1 Identify two points as (x1, y1) and (x2, y2). Adding another 20 g of mass at the end of the spring will give a total mass of 40 g and a length of 8  0.15(20)  11 cm. Use the points (x1, y1)  20, and (x2, y2)  40, to find the linear equation.

(

)

(

)

Step 2 Find the slope of the line. y 2y

All rights reserved.

m 5 x22 2 x11 

Use the slope formula.

11 

Substitute.

40  20

m

,

or

0.15

Simplify.

Step 3 Use one of the points and the point-slope form to write an equation for the line. y  y1  m(x  x1) Use point-slope form. y8

(x  

Substitute. Solve for y.

An equation of the line that models the length of the spring is y 

.

3 Determining Whether a Linear Model Is Reasonable An art expert guessed the selling prices of five paintings. Then, she checked the actual prices. The data points (guess, actual) show the results, where each number is in thousands of dollars. Graph the data points. Decide whether a linear model is reasonable. If so, draw a trend line and write its equation. {(12, 11), (7, 8.5), (10, 12), (5, 3.8), (9, 10)} Actual (thousands $)

© Pearson Education, Inc., publishing as Pearson Prentice Hall.

y

)

y

A linear model seems since the points fall close to a line.

12 8

A possible trend line is the line through (6, 6) and (10.5, 11). Using these two points, the equation in

4

slope-intercept form is y 

O



.

x 4 8 12 Guess (thousands $)

Daily Notetaking Guide

Algebra 2 Lesson 2-4

31

0021_A2_AIOsw07_DNG_ch02.qxd

04/18/07

12:09 pm

Page 32

Name_____________________________________ Class____________________________ Date________________

Quick Check. 1. Suppose a balloon begins descending at a rate of 20 ft/min from an elevation of 1350 ft. a. Write an equation to model the balloon’s elevation as a function of time. What is true about the slope of this line?

All rights reserved.

b. Graph the equation. Interpret the h-intercept.

3. Graph the data points. Decide whether a linear model is reasonable. If so, draw a trend line and write its equation. {(7.5, 19.75), (2, 9), (0, 6.5), (1.5, 3), (4, 1.5)}

32

Algebra 2 Lesson 2-4

Daily Notetaking Guide

© Pearson Education, Inc., publishing as Pearson Prentice Hall.

2. A candle is 7 in. tall after burning for 1 h, and 5 in. tall after burning for 2 h. Write a linear equation to model the height of the candle.

Alggebra 2 2-4 NTG.pdf

There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. Alggebra 2 2-4 ...

144KB Sizes 2 Downloads 142 Views

Recommend Documents

Unit 4 2-24.pdf
Haug, Miles 203635 B 85.00% 3.00 4 2. Hill, Yesenia 205479 B 85.00% 3.00 3 3 3. Ipoma, Kelly 205481 A+ 100.00% 4.00 4 4 4. Jackson, Carmen 620325 D- 61.00% 1.50 2 1. Johnson, LarTerrious 202997 C+ 79.00% 2.67 3 3 2. Johnson, Davisha 560602 C 73.00% 2

2-24-2017 minutes.pdf
Feb 24, 2017 - what sort of service extension would be best. - Bill says ... Zack says TS can send an email out to U-PASS users to make an ... Other Business.

24-2-17 14-32.pdf
Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. 24-2-17 14-32.pdf. 24-2-17 14-32.pdf. Open. Extract. Open with.

galax-B-2-08-24-12-P.pdf
Cruze's to Malibu's ... Plus Luxurious Enclave's to SRX's and Lacrosse's to CTS's. Browse Before You Drive At: www.collinschevrolet.com. NEW. NEW. NEW.

BCC Nepotism (R 2-24-2014).pdf
There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. BCC Nepotism (R 2-24-2014).pdf. BCC Nepotism (R 2-24-2014).pdf. Open. Extract. Open with. Sign In. Main menu

MINISTRY ORDER NO. 24 (2).pdf
Commission on Auditiniteletter dated December 13, 1982, as follows: Average ... MINISTRY ORDER NO. 24 (2).pdf. MINISTRY ORDER NO. 24 (2).pdf. Open.

INTER MODEL PAPER 2 24-Feb-16.pdf
5. Define mericarp. In which plant you find. it? 6. Give the technical description of ovary in. Solanum nigrum. 7. What is the significance of vacuole in a. plant cell?

sample 24 Day challenge_week 2.pdf
There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. sample 24 Day challenge_week 2.pdf. sample 24 Day challenge_week 2.pdf. Open. Extract. Open with. Sign In. M

CatchUp - Wk 2 with appendix pp13-24.pdf
Yellow Collage. Individual: Mini-posters: Yellow Objects. WORK PERIOD 2: Teacher-Supervised: Junk Box Sorting: Yellow/Red Objects. Yellow/Red Chart.

Thorndon Fair Newsletter (24 Nov 2016)(2).pdf
... Society newsle9er and a history of. the Fair's early years. Thanks to Bre9 Mackay for his research. Page 2 of 2. Thorndon Fair Newsletter (24 Nov 2016)(2).pdf.

galax-B-2-08-24-12-P.pdf
CENTER, RECENTLY ANNOUNCED THAT THE HARRIS AND FRANCES ... things that would take a life- time to fully explore. ... galax-B-2-08-24-12-P.pdf.

Organizational Chart-NO NAMES.doc WORD -REVISED 2-24-16.pdf ...
Principals. Administrative. Assistant Director. Child Nutrition. EL Coaches. (5). Staff. Migrant. Nurses/Psychologists. Mental Health. Clinicians. Classified Staff ... Finance Office/. Payroll/. Purchasing/. Warehouse/. Print Shop. Warehouseperson. D

24 Closeted.pdf
There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. 24 Closeted.pdf.

Freeview_Play_Technical_Summary_v6.0_2015-09-24.pdf
relevant OD pages). Providing an opportunity for additional Freeview broadcaster OD services to launch. alongside the core Public Service Broadcaster (PSB) players. 1 Some of these players, such as the BBC iPlayer, also include live streams. Page 3 o

of 24 - Drive
Qualcomm and the Mobile Revolution: Fostering Innovation and Economic Growth. May 16, 2016. Page 1. Whoops! There was a problem loading this page.

24 Vayikra.pdf
There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. 24 Vayikra.pdf.