Copyright © 2012 Pearson Education, Inc. All rights reserved Chapter 1 Linear Functions

Copyright © 2012 Pearson Education, Inc. All rights reserved

Chapter 1

Linear Functions

Copyright © 2012 Pearson Education, Inc. All rights reserved

1.1

Slopes and Equations of Lines

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Figure 1

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Figure 2

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Figure 3

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Your Turn 1

Find the slope of the line through (1,5) and (4,6).

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1 1 2 2 Let ( , ) (1,5) andSol ( ,ut )ion: (4,6). x y x y

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Your Turn 2

Find the equation of the line with x-intercept − 4 and

y-intercept 6.

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Your Turn 3

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Find the slope of the line whose equation is 8 3 5.x y

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Your Turn 4

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Find the equation of the line through (2,9) and (5,3).

Put your answer in slope-intercept form.

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Your Turn 5

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Find the equation of the line that passes through the point (4,5)

and is parallel to the line 3 6 7.x y

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Your Turn 6

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Find the equation of the line that passes through the point (3,2)

and is perpendicular to the line 2 3 4.x y

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Real Life Example

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1.2

Linear Functions and Applications

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Your Turn 1

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Let ( ) 4 5. Find ( 5).g x x g

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Your Turn 2(a)Suppose that Greg Tobin, manager of a giant supermarket

chain, has studied the supply and demand for watermelons. He

has noticed that the demand increases as the price decreases.

He has determined that the quantity (in thousands) demanded

weekly, q, and the price (in dollars) per watermelon, p, are

related by the linear function

(a) Find the quantity of watermelons demanded at a price of $3.30 per watermelon.

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( ) 9 0.75 . Demand functionp D q q

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Your Turn 2(b)

Greg also noticed that the quantity of watermelons supplied

decreased as the price decreased. Price p and supply q are

related by the linear function

(b) Find the quantity of watermelons supplied at a price of $3.30 per watermelon.

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( ) 0.75 . Supply functionp S q q

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Your Turn 3

Find the equilibrium quantity and price for the watermelons

using the demand equation and the supply equation.

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( ) 10 0.85D q q ( ) 0.4 .S q q

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Figure 11

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Figure 12

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Your Turn 4

The marginal cost to make x batches of a prescription

medication is $15 per batch, while the cost to produce 80

batches is $1930. Find the cost function C(x), given that it is linear.

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Your Turn 5A firm producing poultry feed finds that the total cost C(x) in

dollars of producing x units is given by

Management plans to charge $58 per unit for the feed.

How many units must be sold to produce a profit of $8030?

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( ) 35 250.C x x

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Figure 13

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Figure 14

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