<< 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
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x 21 25 30 31 40 50
y 17 11 2 –1 –18 –40

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

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x y
100 2000
80 1798
60 1589
55 1580
40 1390
20 1202
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x 900 988 1000 1010 1200 1205
y 70 80 82 84 105 108

y = 0. 121 x 38.841 , r = 0.998

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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.

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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.

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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.

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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.

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

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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

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Predict when the population will hit 8,000.

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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

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Predict when the profit will exceed one million dollars.

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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

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

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Chapter review exercises

Linear Functions

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

Yes

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Questions & Answers

0.037 than find sin and tan?
Jon Reply
cos24/25 then find sin and tan
Deepak Reply
tan20?×tan40?×tan80?
Santosh Reply
At the start of a trip, the odometer on a car read 21,395. At the end of the trip, 13.5 hours later, the odometer read 22,125. Assume the scale on the odometer is in miles. What is the average speed the car traveled during this trip?
Kimberly Reply
-3 and -2
Julberte Reply
tan(?cosA)=cot(?sinA) then prove cos(A-?/4)=1/2?2
Chirag Reply
tan(pi.cosA)=cot(?sinA) then prove cos(A-?/4)=1/2?2
Chirag Reply
sin x(1+tan x)+cos x(1+cot x) = sec x +cosec
Ankit Reply
let p(x)xq
Sophie Reply
To the nearest whole number, what was the initial population in the culture?
Cheyenne Reply
do posible if one line is parallel
Fran Reply
The length is one inch more than the width, which is one inch more than the height. The volume is 268.125 cubic inches.
Vamprincess Reply
Using Earth’s time of 1 year and mean distance of 93 million miles, find the equation relating ?T??T? and ?a.?
James Reply
cos(x-45)°=Sin x ;x=?
Samaresh Reply
10-n ft
Nalin Reply
Practice Key Terms 5

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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