1. Find the distance between the following two points
Find the distance between the following two points. Then find the coordinates of the midpoint between them.

2. Find the distance between the following two points
Find the distance between the following two points. Then find the coordinates of the midpoint between them.
d = 10
Midpoint is (1, -1)

3. A Review of Linear Functions
Linear Function (aka Linear Equation): Establishes a consistent relation between 2 parameters (x and y). When these (x, y) pairs are plotted on a coordinate plane, they line up in a straight line.
Example: means that for any value of x, the corresponding value of y can be found by multiplying x by , then adding 2 to that product.

4. Let’s find some ordered pairs that follow this relation.
First, pick some values of x. How about the following:

9. Plot these points on a graph.
What is special about this group of points?

10. Some Important Details
Slope – The rate of change in y for every unit change in x.
What does this mean?

11. An Explanation of Slope

12. An Explanation of Slope

13. An Explanation of Slope

14. Independent and Dependent Variables
We frequently refer to x as the independent variable
We frequently refer to y as the dependent variable
This is because YOU choose the value for x and use it to calculate the value of y

15. Find 3 ordered pairs that are solutions to each linear equation

16. Find the slope

17. Find the slope

18. Find the slope

19. Find the slope 19

20. Homework Quiz Wednesday Pg 409-410 #1-8 even,
#14 – 20 even, (do not graph)
#37, #38,
#42-46 even 20

21. Warm Up Tues. Sep 14
Find 3 ordered pairs that are solutions to the following equation.
Find the slope. Find the x and y intercepts 21

22. Warm Up Tues. Sep 14 22

23. Tue Sep 14 HW Solutions

24. Tue Sep 14 HW Solutions

25. Day2 Linear Function Applications
Linear functions are frequently presented in Standard Form:
Therefore, we must know how to rewrite the equation in slope intercept form:

26. Convert from standard form to slope intercept form.

28. Linear Function Applications
Sometimes it is useful to write out and solve a linear function that models a real world situation

29. Car Rental
A car rental company charges a flat fee of $35 plus $25 for each day that the car is rented. Write out a linear function to represent the total cost, y, to rent a car for x days

30. Car Rental
A car rental company charges a flat fee of $35 plus $25 for each day that the car is rented. Write out a linear function to represent the total cost, y, to rent a car for x days

31. Telephone Company
The telephone company charges a monthly service charge of $ They also charge a usage charge of $0.07 per minute of calling. Write out a linear function to represent the total cost each month, f(x), to talk on the phone for x minutes a month.

32. Telephone Company
The telephone company charges a monthly service charge of $ They also charge a usage charge of $0.07 per minute of calling. Write out a linear function to represent the total cost each month, f(x), to talk on the phone for x minutes a month.

33. Pg #55-64
55. Suppose that a taxicab driver charges $1.50 per mile. Let x represent the number of miles driven and f(x) represent the total charge.
f(x)=
f(0) =
f(1 )=
f(2) =
f(3) =

34. Pg #55-64
55. Suppose that a taxicab driver charges $1.50 per mile. Let x represent the number of miles driven and f(x) represent the total charge.
f(x)=
f(0) = $0.00
f(1 )= $1.50
f(2) = $3.00
f(3) = $4.50 34

35. 56. Cost to Mail a Package Suppose that a package weighing x pounds costs f(x) dollars to mail to a given location, where
f(x) = 2.75x.
(a) What is the value of f(3)?
(b) Describe what 3 and the value f(3) mean in part (a), using the terminology independent variable and dependent variable.
(c) How much would it cost to mail a 5-lb package? Write the answer using function notation.

36. What is the value of f(3)? $8.25
56. Cost to Mail a Package Suppose that a package weighing x pounds costs f(x) dollars to mail to a given location, where
f(x) = 2.75x.
What is the value of f(3)? $8.25
(b) Describe what 3 and the value f(3) mean in part (a), using the terminology independent variable and dependent variable. 3 represents 3 lbs. f(3) represents the cost
(c) How much would it cost to mail a 5-lb package? Write the answer using function notation. f(5) = $13.75 36

37. (a) Find the height of a man with a femur measurement of 56 cm
57. Forensic Studies - Forensic scientists use the lengths of the tibia (t), the bone from the ankle to the knee, and the femur (r), the bone from the knee to the hip socket, to calculate the height of a person. A person’s height (h) is determined from the lengths of these bones using functions defined by the following formulas. All measurements are in centimeters.
(a) Find the height of a man with a femur measurement of 56 cm
(b) Find the height of a man with a tibia measurement of 40 cm
(c) Find the height of a woman with a femur measurement of 50 cm
(d) Find the height of a woman with a tibia measurement of 36 cm

38. Find the height of a man with a femur measurement of 56 cm 194.53 cm
57. Forensic Studies - Forensic scientists use the lengths of the tibia (t), the bone from the ankle to the knee, and the femur (r), the bone from the knee to the hip socket, to calculate the height of a person. A person’s height (h) is determined from the lengths of these bones using functions defined by the following formulas. All measurements are in centimeters.
Find the height of a man with a femur measurement of 56 cm cm
Find the height of a man with a tibia measurement of 40 cm cm
(c) Find the height of a woman with a femur measurement of 50 cm cm
Find the height of a woman with a tibia measurement of 36 cm cm 38

39. 58. Pool Size for Sea Otters - Federal regulations set standards for the size of the quarters of marine mammals. A pool to house sea otters must have a volume of “the square of the sea otter’s average adult length (in meters) multiplied by 3.14 and by .91 meter” If x represents the sea otter’s average adult length and f(x) represents the volume of the corresponding pool size, this formula can be written as
Find the volume of the pool for each of the following adult lengths (in meters). Round answers to the nearest hundredth.
(a) .8 (b) (c) (d) 1.5

40. 58. Pool Size for Sea Otters - Federal regulations set standards for the size of the quarters of marine mammals. A pool to house sea otters must have a volume of “the square of the sea otter’s average adult length (in meters) multiplied by 3.14 and by .91 meter” If x represents the sea otter’s average adult length and f(x) represents the volume of the corresponding pool size, this formula can be written as
Find the volume of the pool for each of the following adult lengths (in meters). Round answers to the nearest hundredth.
(a) .8 (b) (c) (d) 1.5
1.83m m m m3 40

41. 59. Number of Post Offices The linear function
f(x) = —183x + 40,034
is a model for the number of U.S. post offices for the period 1990—1995, where x = 0 corresponds to 1990, x = 1 corresponds to 1991, and so on. Use this model to give the approximate number of post offices during the following years. (Source: U.S. Postal Service, Annual Report of the Postmaster General and Comprehensive Statement on Postal Operations.)
(a) (b) (c) 1995

42. 59. Number of Post Offices The linear function f(x) = —183x + 40,034
is a model for the number of U.S. post offices for the period 1990—1995, where x = 0 corresponds to 1990, x = 1 corresponds to 1991, and so on. Use this model to give the approximate number of post offices during the following years. (Source: U.S. Postal Service, Annual Report of the Postmaster General and Comprehensive Statement on Postal Operations.)
(a) (b) (c) 1995
39, , ,119 42

43. is a model for U.S. defense budgets in millions of dollars from 1992 to 1996, where x = 0 corresponds to 1990, x = 2 corresponds to 1992, and so on. Use this model to approximate the defense budget for the following years:
(a) (b) (c) 1996

44. is a model for U.S. defense budgets in millions of dollars from 1992 to 1996, where x = 0 corresponds to 1990, x = 2 corresponds to 1992, and so on. Use this model to approximate the defense budget for the following years:
1993 (b) (c) 1996
$286,322 million $286,322 million $286,322 million

45. 61. Perian Herring stuffs envelopes for extra income during her spare time. Her initial cost to obtain the necessary information for the job was $200. Each envelope costs $0.02 and she gets paid $0.04 per envelope stuffed. Let x represent the number of envelopes stuffed? Write an equation to represent this scenario.

46. 61. Perian Herring stuffs envelopes for extra income during her spare time. Her initial cost to obtain the necessary information for the job was $200. Each envelope costs $0.02 and she gets paid $0.04 per envelope stuffed. Let x represent the number of envelopes stuffed? Write an equation to represent this scenario.

47. 62. Tony Motton runs a copying service from his home
62. Tony Motton runs a copying service from his home. He paid $3500 for the copier and a lifetime service contract. Each sheet of paper he uses costs $0.01 and he charges $0.05 per copy he makes. Write an equation to represent this scenario. Remember to define your variables.

48. 62. Tony Motton runs a copying service from his home
62. Tony Motton runs a copying service from his home. He paid $3500 for the copier and a lifetime service contract. Each sheet of paper he uses costs $0.01 and he charges $0.05 per copy he makes. Write an equation to represent this scenario. Remember to define your variables.

49. 63. Eugene Smith operates a delivery service in a southern city
63. Eugene Smith operates a delivery service in a southern city. His start-up costs amounted to $ He estimates that is costs him $3.00 per delivery and he charges $5.50 per delivery. Write an equation to represent this scenario. Remember to define your variables.

50. 63. Eugene Smith operates a delivery service in a southern city
63. Eugene Smith operates a delivery service in a southern city. His start-up costs amounted to $ He estimates that is costs him $3.00 per delivery and he charges $5.50 per delivery. Write an equation to represent this scenario. Remember to define your variables.

51. 64. Lisa Ventura bakes cakes and sells them at county fairs
64. Lisa Ventura bakes cakes and sells them at county fairs. Her initial cost for the Washington County Fair in 1996 was $ She figures that each cake costs $2.50 to make, and she charges $6.50 per cake. Let x represent the number of cakes sold. (Assume that there were no cakes left over). Write an equation that represents this scenario.

52. Pg 410 #47

53. a) students/year

54. +232 students/year
Positive; Increase

55. +232 students/year
Positive; Increase

57. d) students/year

58. -1.66 students/year
Negative; Decreased

59. -1.66 students/year
Negative; Decreased
1.66 students per year

60. Homework
Page 411 #63 – 65. Hand In