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.

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)

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.

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

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

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

An Explanation of Slope

An Explanation of Slope

An Explanation of Slope

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

Find 3 ordered pairs that are solutions to each linear equation

Find the slope

Find the slope

Find the slope

Find the slope 19

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

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

Warm Up Tues. Sep 14 22

Tue Sep 14 HW Solutions

Tue Sep 14 HW Solutions

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:

Convert from standard form to slope intercept form.

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

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

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

Telephone Company The telephone company charges a monthly service charge of $12.95. 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.

Telephone Company The telephone company charges a monthly service charge of $12.95. 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.

Pg 433-434 #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) =

Pg 433-434 #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

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.

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

(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

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 194.53 cm Find the height of a man with a tibia measurement of 40 cm 177.29 cm (c) Find the height of a woman with a femur measurement of 50 cm 194.53 cm Find the height of a woman with a tibia measurement of 36 cm 163.65 cm 38

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) 1.0 (c) 1.2 (d) 1.5

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) 1.0 (c) 1.2 (d) 1.5 1.83m3 2.86m3 4.11m3 6.43m3 40

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) 1991 (b) 1993 (c) 1995

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) 1991 (b) 1993 (c) 1995 39,851 39,485 39,119 42

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) 1993 (b) 1995 (c) 1996

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) 1995 (c) 1996 $286,322 million $286,322 million $286,322 million

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.

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.

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.

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.

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 $2300. 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.

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 $2300. 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.

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 $40.00. 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.

Pg 410 #47

a) +232 students/year

+232 students/year Positive; Increase

+232 students/year Positive; Increase

d) -1.66 students/year

-1.66 students/year Negative; Decreased

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

Homework Page 411 #63 – 65. Hand In