1. Chapter 1
Linear Functions
Table of Contents
1.1 Solving Linear Equations
1.2 Using Data to Create Scatterplots
1.3 Fundamentals of Graphing and Slope
1.4 Intercepts and Graphing
1.5 Finding Equations of Lines
1.6 Finding Linear Models
1.7 Functions and Function Notation

2. Review of Linear Equations

3. What to expect
• In this chapter we are going to translate word
problems into equations of lines
• We will then graph those lines and find useful
properties of those lines
• We will then use those properties to analyze
what is happening in the physical situation to
give the numbers meaning

4. Golf Carts To Go sells refurbished golf carts in south Florida. The
company has fixed costs of $26,000 per month for rent, salary and
utilities. They can buy used carts and refurbish them for an
average of $1,400 each. They sell the carts for an average price of
$2500 each. Golf Carts To Go can only refurbish 55 carts a month.
a. Write an equation for the monthly cost of refurbishing n carts.
b. Write an equation for the monthly revenue from selling golf
carts.
c. Write an equation for the monthly profit the company makes if
they refurbish and sell n carts.
d. What is the profit of refurbishing and selling 25 golf carts?
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5. Golf Carts To Go sells refurbished golf carts in south Florida. The
company has fixed costs of $26,000 per month for rent, salary and
utilities. They can buy used carts and refurbish them for an
average of $1,400 each. They sell the carts for an average price of
$2500 each. Golf Carts To Go can only refurbish 55 carts a month.
e. what is the fewest number of golf carts that the company can
physically or reasonably make?
f. What is the most golf carts that the company can physically or
reasonably make?
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6. Equations for Business Models
• Costs = Variable Costs + Fixed Costs
– variable cost increase as I make/buy more of
something
• cost of $.5 per phone case made
– fixed costs do not change no matter how much is
made/bought
• rent, utilities, wages [sometimes], loans, ect.

7. Equations for Business Models
• Revenue = Price * Quantity
– this is how much money comes in from sales
– gross reciepts

8. Equations for Business Models
• Profit = Revenue – Cost
• Profit = Revenue – Variable Cost – Fixed Cost
– this is what is left over for the business
– how much was actually made

9. An equation for the total cost, C, in dollars for purchasing L lunch
coolers is .
a. Create a table of points that satisfy this equation.
Use 0, 50, 100, & 150.
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45 3C L
Lunch Coolers Cost

10. An equation for the total cost, C, in dollars for purchasing L lunch
coolers is .
b. Create a graph for the equation using your points. Label your
graph with units.
1.3-2
45 3C L
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11. Use the graph to estimate the slope of the line and
determine if the line is increasing or decreasing.
y=x y=-x
11
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12. Use the graph to estimate the slope of the line and
determine if the line is increasing or decreasing.
Determine if it is “steeper” or “flatter”.
y=4x y= ¼ x
12
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13. Use the graph to estimate the slope of the line and
determine if the line is increasing or decreasing.
Determine if it is “steeper” or “flatter”
y=3x y= -⅓x
13
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14. Determine if the points given in the table all lie on a line.
a.
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x y
6 11
10 16
12 18.5
22 31

15. Determine if the points given in the table all lie on a line.
b.
1.3-5
x y
5.4
2 3.4
4 2.8
8 1
3
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16. 1.3-616 Back to Table of Contents

17. Let be the total cost in dollars to produce p
pizzas a day at a local pizzeria.
a. describe “C”
b. describe 4.5
c. describe “p”
d. describe 1200
1.3-7
4.5 1200C p
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18. Let be the total cost in dollars to produce p
pizzas a day at a local pizzeria.
e. Now that you now the Cost what might you ask?
f. How could you model it?
g. What math should you now perform to answer important
questions
1.3-7
4.5 1200C p
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19. Let be the percentage of adults aged 18
years old and over in the United States that have been
diagnosed with diabetes, t years since 2000. Source: CDC.
a. Describe “D”
b. Describe .28
c. Describe “t”
d. Describe 5.95
e. What is the upper limit where the model breaks down
f. what is the lower limit where the model breaks down
1.3-7
0.28 5.95D t
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20. Sketch the graph of the following lines. Label the vertical
intercept.
a. b.
1.3-8
3
6
4
y x 2 7y x
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21. Find the intercepts and graph the line
1.4-4
2 3 18x y
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22. Sketch the graph of the following lines
a.
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4x

23. Sketch the graph of the following lines
b.
1.4-5
1.5y
23

24. A business purchased a production machine in 2005 for $185,000.
For tax purposes, the value of the machine in 2011 was $129,500.
If the business is using straight line depreciation, write the
equation of the line that gives the value of the machine based on
the age of the machine in years.
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25. Using the value of the production machine equation we found
earlier, answer the following:
a. What is the slope of the equation? What does it represent in
regards to the value of the machine?
b. What is the vertical intercept of the equation? What does it
represent in this situation?
1.5-7
9250 185,000v a
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26. Using the value of the production machine equation we found
earlier, answer the following:
c. What is the horizontal intercept of the equation? What does it
represent in this situation?
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9250 185,000v a

27. According to www.childtrendsdatabank.org the number of newly
diagnosed AIDS cases for adolescents 13-19 years old in the
United States was 310 in 2000 and 458 in 2003. Assume that the
number of cases is growing at a constant rate, and write an
equation to represent this situation.
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28. Using the AIDS equation found in classroom example 3, answer
the following:
a. What is the slope of the equation? What does it mean in this
situation?
b. What is the vertical intercept for the equation? What does it
represent in this situation?
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49.3 310C t

29. There were 44.1 million major home appliances shipped in the
United States in 2007. In 2009 only 36.7 million were shipped.
Source: Association of Home Appliance Manufacturers.
a. Write an equation for the number of major home appliances
shipped in the US t years since 2000.
b. What is the slope of the equation found in part a? What does it
represent?
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30. There were 44.1 million major home appliances shipped in the
United States in 2007. In 2009 only 36.7 million were shipped.
Source: Association of Home Appliance Manufacturers.
c. What is the vertical intercept for the equation you found in
part a? What does it represent?
1.5-9
3.7 70A t
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31. a. Write the equation of the line that passes through the points in
the table.
1.5-5
x y
5 13
7 15.8
15 27
18 31.2
31

32. b. Write the equation of the line shown in the graph.
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33. Special Types of Lines
Parallel Perpendicular
33

34. Special Types of Lines
Parallel Perpendicular
34

35. a. Write the equation of the line that goes through the point
and is perpendicular to the line .
1.5-6
4 23y x( 12,8)
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36. b. Write the equation of the line that goes through the point (8,11)
and is parallel to the line .
1.5-6
5 2 30x y
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37. Create a scatter plot on your graphing calculator for the
population data for North Carolina given in the table.
Source: Population Division, U.S. Census Bureau
Find an equation for a model of the population of North Carolina
data given earlier.
1.6-1
Year
Population
(millions)
2003 8.41
2004 8.52
2005 8.66
2006 8.85
2007 9.04
2008 9.22
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38. 38

39. The total revenue for GE is given in the table.
Source: GE 2008 annual report
a. Find an equation for a model of these data.
1.6-3
Year
Revenue
(billions $)
2004 124
2005 136
2006 152
2007 172
2008 183
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40. The total revenue for GE is given in the table.
b. Using your model estimate GE’s revenue
in 2010.
c. What is the slope of your model? What does it mean in regards
to GE’s revenue?
d. Determine a reasonable domain and range for the model.
1.6-3
Year Revenue (billions $)
2004 124
2005 136
2006 152
2007 172
2008 183
40
14.75 65R t
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41. Determine whether the following descriptions of relations are
functions or not.
a. The set
b.
c. Weekly salaries during the mth month of the year.
1.7-1
(2,5),(4,8),(10,8),(20,15)A
Day of week Monday Wednesday Saturday Monday
Temperature
degrees
Fahrenheit
90 88 91 93
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42. a. Is the equation a function or not?
b. Is the equation a function or not?
1.7-2
7 20y x
2 2
4 16y x
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43. c. Does the graph represent a function?
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44. = The height of a toy rocket in feet t second after launch is
given by
H(t) = 100t – 4.9 t2
Interpret the following mathematical statements:
a. H(0)
b. H(4)
c. H(6)
1.7-3
( )H t
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45. Let
Find the following.
a.
1.7-5
2
( ) 7 2 ( ) 1.25 14 ( ) 2 10f x x g x x h x x
(3)f
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46. Let
Find the following.
b.
1.7-5
2
( ) 7 2 ( ) 1.25 14 ( ) 2 10f x x g x x h x x
(5)h
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47. Let
Find the following.
c. x such that
1.7-5
2
( ) 7 2 ( ) 1.25 14 ( ) 2 10f x x g x x h x x
( ) 15g x
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48. Use the graph to estimate the following.
a.
b. x such that
1.7-6
(2)f
( ) 5f x
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49. What is Domain and Range for a Model?
Domain
• the smallest value that is
reasonable is the beginning
of the Domain
– avoid making negative objects
– avoid losing money
• the largest possible value
that is reasonable is the end
of the Domain
– avoid making infinite objects
– avoid making infinite money
• If you are given data, do not
stray to far away
Range
• Enter the smallest value
from the Domain and that
gives you one endpoint of
the Range
• Enter the largest value from
the Domain and that is the
other endpoint of the Range
49

50. !WARNING!
• The Domain and Range of a Line are
DIFFERENT than the Domain and Range of a
Model!
– A Line is a mathematical object without physical
meaning or constraint
– A Model uses a mathematical object to assist in
analysis that has physical meaning and constraints

51. Create a scatterplot of the data given in the table.
The percent of adults aged 20
years and over in the United
States who are considered obese
are given in the table.
Source: CDC 2008 National Health Interview Survey.
1.2-1
Year Percent
2004 24.5
2005 25.4
2006 26.4
2007 26.7
2008 26.8
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52. a. Using the scatterplot of the obesity data from before, draw an
“eyeball best fit” line through the data.
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53. 1.2-1
b. Using your eyeball best-fit line, make a prediction for the
percentage of adults in the United States who were considered
obese in 2010.
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54. Determine a reasonable domain and range for the graphical
model found for the obesity data.
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55. Use the graph to answer the following questions
a. Estimate the vertical
intercept.
b. Estimate the horizontal
intercept.
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56. Use the graph to answer the following questions
c. Estimate the input value that
makes the output of this
graph equal 3.
d. Estimate the output value of
this graph when the input
value is .
1.2-3
2
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57. The percentage of students in twelfth grade who report smoking
daily is given in the table. Source: www.monitoringthefuture.org
a. Create a scatterplot for these data and
draw an “eyeball best fit” line through the
data.
1.2-5
Year Percent
2000 20.6
2001 19.0
2002 16.9
2003 15.8
2004 15.6
2005 13.6
2006 12.2
57

58. Answer: t = years since 2000. P = percent of twelfth grade students
who report smoking daily.
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59. b. Determine the vertical
intercept for this model.
Explain its meaning in this
situation.
c. Find a reasonable domain
and range for this model.
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60. d. According to your graphical
model, what percentage of
twelfth grade students
reported smoking daily in
2007?
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61. Determine the domain and range of the following functions
a.
b.
1.7-7
( ) 3 7f x x
( ) 8g x
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62. The population of Wisconsin, in millions, is given in the table.
Source: www.census.gov
Let P(t) be the population of
Wisconsin, in millions,
t years since 2000.
a. Find an equation for a model
of these data. Write your
model in function notation.
b. Determine a reasonable domain and range for your model.
1.7-4
Year
Population
(in millions)
2003 5.47
2004 5.51
2005 5.54
2006 5.57
2007 5.60
2008 5.63
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63. The population of Wisconsin, in millions, is given in the table.
Source: www.census.gov
c. Find P(14) and interpret its
meaning in regard to the
population of Wisconsin.
d. Find when P(t) = 5.75 and interpret its meaning in regard to
the population of Wisconsin.
1.7-4
Year
Population
(in millions)
2003 5.47
2004 5.51
2005 5.54
2006 5.57
2007 5.60
2008 5.63
63
( ) 0.03 5.39P t t
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