<< Chapter < Page Chapter >> Page >
x y
4 44.8
5 43.1
6 38.8
7 39
8 38
9 32.7
10 30.1
11 29.3
12 27
13 25.8
Got questions? Get instant answers now!
x 21 25 30 31 40 50
y 17 11 2 –1 –18 –40

y = 1 . 981 x + 6 0. 197; r = 0. 998

Got questions? Get instant answers now!
x y
100 2000
80 1798
60 1589
55 1580
40 1390
20 1202
Got questions? Get instant answers now!
x 900 988 1000 1010 1200 1205
y 70 80 82 84 105 108

y = 0. 121 x 38.841 , r = 0.998

Got questions? Get instant answers now!

Extensions

Graph f ( x ) = 0.5 x + 10. Pick a set of five ordered pairs using inputs x = −2 , 1 , 5 , 6 , 9 and use linear regression to verify that the function is a good fit for the data.

Got questions? Get instant answers now!

Graph f ( x ) = 2 x 10. Pick a set of five ordered pairs using inputs x = −2 , 1 , 5 , 6 , 9 and use linear regression to verify the function.

( −2 , −6 ) , ( 1 , −12 ) , ( 5 , −20 ) , ( 6 , −22 ) , ( 9 , −28 ) ; Yes, the function is a good fit.

Got questions? Get instant answers now!

For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span, (number of units sold, profit) for specific recorded years:

( 46 , 1 , 600 ) , ( 48 , 1 , 55 0 ) , ( 50 , 1 , 505 ) , ( 52 , 1 , 54 0 ) , ( 54 , 1 , 495 ) .

Use linear regression to determine a function P where the profit in thousands of dollars depends on the number of units sold in hundreds.

Got questions? Get instant answers now!

Find to the nearest tenth and interpret the x -intercept.

( 189 .8 , 0 ) If 18,980 units are sold, the company will have a profit of zero dollars.

Got questions? Get instant answers now!

Find to the nearest tenth and interpret the y -intercept.

Got questions? Get instant answers now!

Real-world applications

For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs shows the population and the year over the ten-year span, (population, year) for specific recorded years:

( 25 00 , 2000 ) , ( 265 0 , 2001 ) , ( 3000 , 2003 ) , ( 35 00 , 2006 ) , ( 42 00 , 2010 )

Use linear regression to determine a function y , where the year depends on the population. Round to three decimal places of accuracy.

y = 0.00587 x + 1985 .4 1

Got questions? Get instant answers now!

Predict when the population will hit 8,000.

Got questions? Get instant answers now!

For the following exercises, consider this scenario: The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of over the ten year span, (number of units sold, profit) for specific recorded years:

( 46 , 25 0 ) , ( 48 , 3 05 ) , ( 50 , 35 0 ) , ( 52 , 39 0 ) , ( 54 , 41 0 ) .

Use linear regression to determine a function y , where the profit in thousands of dollars depends on the number of units sold in hundreds.

y = 2 0. 25 x 671 . 5

Got questions? Get instant answers now!

Predict when the profit will exceed one million dollars.

Got questions? Get instant answers now!

For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs show dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span (number of units sold, profit) for specific recorded years:

( 46 , 25 0 ) , ( 48 , 225 ) , ( 50 , 2 05 ) , ( 52 , 18 0 ) , ( 54 , 165 ) .

Use linear regression to determine a function y , where the profit in thousands of dollars depends on the number of units sold in hundreds.

y = 1 0. 75 x + 742 . 5 0

Got questions? Get instant answers now!

Predict when the profit will dip below the $25,000 threshold.

Got questions? Get instant answers now!

Chapter review exercises

Linear Functions

Determine whether the algebraic equation is linear. 2 x + 3 y = 7

Yes

Got questions? Get instant answers now!
Practice Key Terms 5

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College algebra' conversation and receive update notifications?

Ask