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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

Why is b in the answer
Dahsolar Reply
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Brad Reply
answer
Ernest
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Nitin
(Pcos∅+qsin∅)/(pcos∅-psin∅)
John Reply
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Amoah
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Chabelita Reply
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Chabelita
solve for X,,4^X-6(2^)-16=0
Alieu Reply
x4xminus 2
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t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
ZAHRO Reply
If  , , are the roots of the equation 3 2 0, x px qx r     Find the value of 1  .
Swetha Reply
Parts of a pole were painted red, blue and yellow. 3/5 of the pole was red and 7/8 was painted blue. What part was painted yellow?
Patrick Reply
Parts of the pole was painted red, blue and yellow. 3 /5 of the pole was red and 7 /8 was painted blue. What part was painted yellow?
Patrick
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Katleho Reply
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?
Mary Reply
23yrs
Yeboah
lairenea's age is 23yrs
ACKA
hy
Katleho
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Katleho
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christopher
solve for X, 4^x-6(2*)-16=0
Alieu
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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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