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