2. Rate of Change from a Situation
A plumber charges $50 to make a house call. He also charges $25.00 per hour for labor. A. Rate of Change: _____________ Beginning: _________________ B. Write an equation that you could use to the amount a plumber charges for a house call based on the number of hours of labor. ___________________ C. How much would it cost for a house call that requires 4 hours of labor? D. If the bill from the plumber is $275, how many hours did the plumber work at your house? 25
Slope, m 50
y-intercept, b
y = 25x + 50
y = 25(4) + 50
y = $ 150
275 = 25x + 50
x = 9 hours

3. Graph the equation y = 25x + 50 to represent the situation.
300
250
200
150
100 50
Cost
Time
Where on your graph do you find that 4 hours of labor costs $150?
Name the coordinates of that point.
Where on your graph do you find that 9 hours of labor costs $275?
Name the coordinates of that point.

4. y = x + 3 y = (8) +3 y = $11 15 = x + 3 x = 12 miles
You are visiting Baltimore, MD and a taxi company charges a flat fee of $3.00 for using the taxi and $1 per mile.
A. Rate of Change (m): _______________ Beginning (b): ____________
B. Write an equation that you could use to find the cost of the taxi ride in Baltimore, MD. Let x represent the number of miles and y represent the total cost ___________________
C. How much would a taxi ride for 8 miles cost?  
D. If a taxi ride cost $15, how many miles did the taxi travel?
slope, m
3 y-intercept, b
y = x + 3
y = (8) +3
y = $11
15 = x + 3
x = 12 miles

5. Graph the equation y = x + 3 to represent the situation. 30 25 20 15 10 5
Cost
Number of Miles
Where on your graph do you find that an 8 mile taxi ride costs $11?
Name the coordinates of that point.
Where on your graph do you find that you can travel 12 miles in the taxi for $15?
Name the coordinates of that point.

7. Warm Up
For the table below, calculate the unit rate and determine if the table represents a linear relationship. x -2 2 4 6 y -8 -4 8
Unit rate _________________
Linear relationship ____yes ____ no
Hint: change in y
change in x

8. Standard to Slope-Intercept Form & Point-Slope Form

9. Slope-Intercept Form
y = mx + b
Example: y = -3x + 5

10. Standard Form
Ax + By = C
Example: 3x + 2y = 8

11. Standard Form to Slope-intercept Ax + By = C y = mx + b
3𝑥+𝑦=4 −3𝑥 −3𝑥 𝑦=−3𝑥+ 4 In Slope Intercept form, the coefficient of y must be positive!!!

12. Slope Intercept to Standard Form y = mx + b Ax + By = C
𝑦=−3𝑥+4 +3𝑥 +3𝑥 3𝑥+𝑦=4 In Standard Form, the coefficient of x cannot be negative or a fraction.

13. Practice Write in slope-intercept form y = mx + b
6𝑥=4𝑦 x + 16 = - 4y

14. Practice Write in Standard form Ax + By = C
y = 4x −2𝑥=10𝑦+12

18. Write in slope-intercept form.
𝑎. 4 𝑥+8𝑦 −2=0 𝑏. 14𝑦=2𝑥+18 c. 9𝑦=12𝑥 −35 d. 12𝑥−36𝑦−24=0 𝑒. 3𝑥=−5𝑦+1 𝑓. 10𝑥=2𝑦 −8

19. Organize and Match the problems
Convert your problem to the opposite form.
(slope intercept form to standard OR standard to slope intercept form)

20. Check Up!!! Write each equation in slope intercept form. 1. 3𝑦=9𝑥+6
1. 3𝑦=9𝑥+6
2. 5𝑦=3𝑥−10
3. 5𝑥 −4=3𝑦+2
𝑦=𝑥
Write an equation in point slope form, and then convert into slope intercept form.
5. slope of 2;(3,4)
6. slope of −4;(−3,1)

21. Practice
EX 3 : 5𝑥=−10𝑦+3

22. Practice
EX 4 : 8𝑥−21𝑦+13=0

23. Practice
EX 5 : 𝑠𝑙𝑜𝑝𝑒 3, (2,6)

24. Practice
EX 6 : 𝑠𝑙𝑜𝑝𝑒 1 5 , (−4,−2)

27. Point-Slope Form 𝑦−𝑦1=𝑚(𝑥−𝑥1) Example: m=-3 and the point (1,2)
𝑦−2 = −3 𝑥−1
EXTREMELY HELPFUL IF YOU ARE GIVEN SLOPE AND ONE POINT!!!! hint hint

28. slope of −2;(−3,4)
slope of 1 3 ;(3,−4)

29. Working in the book… Page 528-534
What you do not finish in class is for homework

30. Perpendicular and Parallel Lines
November 6th, 2014

31. Perpendicular Lines
The slopes of perpendicular lines are opposite reciprocals.
𝑦=2𝑥+7 𝑎𝑛𝑑 𝑦=− 1 2 𝑥 −4
Slopes are opposite reciprocals

32. Parallel Lines
The slopes of parallel lines are the same and the y-intercepts are different.
𝑦=2𝑥+7 𝑎𝑛𝑑 𝑦=2𝑥 −4
Slopes are the same

33. Ex 1:
Write an equation in slope-intercept form of a line parallel to 𝑦=3𝑥 −7 with a y-intercept of 4.
What is the slope or m?
What will the slope or m be in the new equation?
What is the y-intercept or b?

34. Ex 2:
Write an equation in slope-intercept form of a line perpendicular to 𝑦=3𝑥+2 with a y-intercept of 4.
What is the slope or m?
What will the slope or m be in the new equation?
What is the y-intercept or b?

35. Ex 3:
Write an equation in slope-intercept form of a line perpendicular to 𝑦=4𝑥+2 with a y-intercept of 6.
What is the slope or m?
What will the slope or m be in the new equation?
What is the y-intercept or b?

36. Ex 4:
Write an equation in point slope form for the line that contains the point (4,5) and that is perpendicular to the line 2x + 3y = 7.
What will the new slope be?
What is the formula for point-slope form?
Plug in what you know
Solve and put into slope-intercept form.

37. Ex 5:
Write an equation in point slope form for the line that contains the point (3,-2) and that is perpendicular to the line 4x – 2y = -6
What will the new slope be?
What is the formula for point-slope form?
Plug in what you know
Solve and put into slope-intercept form.

38. Practice
Page 91 and 92 on your own paper May do all odd or all even *Your partner must work the same questions as you!

39. Check UP!!! Write an equation of a line that is parallel to
1) 𝑦=2𝑥+7, y-intercept of 4
2) 3𝑥−6𝑦=12, y-intercept of 7
Write an equation of a line that is perpendicular to
3) 𝑦=2𝑥+7, y-intercept of 4
4) 3𝑥−6𝑦=12, y-intercept of 7
Write an equation in point-slope form for the line that contains the point (4,5) and is perpendicular to the graph of the equation
5) 2𝑥+3𝑦=4
6) 𝑥 – 3𝑦 = 8

40. Working in the book… Pages 535-539
What you do not finish in class is for homework

41. Word Problem Practice
November 7th, 2014

42. Page 81 and 87

43. Around the room practice

44. Desk 1
Ismael started the day with an irrigation pipe 120 feet long. He used the equation L = 15s to determine the total length of the pipe as new sections of pipe, s, were welded on to the end.
What is the slope of the line?
What does the slope represent in the context of the problem?

45. Desk 2 Farmer Ali had a well on his property 200 feet deep
Desk 2 Farmer Ali had a well on his property 200 feet deep. When the well went dry, he hired a company to drill the well deeper. He used the equation d = -75t – 200 to find the depth of the well, d, using the number of days the company drilled, t. What is the slope of the line? What does the slope represent in the context of the problem?

46. Desk 3
It costs Corporal Motors $500,000 to outfit their new car line. The company used the equation p = 2500c – 500,000 to determine the amount of profit, p, earned from the sale of cars, c.
What is the slope of the line?
What does the slope represent in the context of the problem?

47. Desk 4 Christopher had $125 in his savings account to buy a used car
Desk 4 Christopher had $125 in his savings account to buy a used car. He used the equation A = 50w to determine the amount in his savings, A, after depositing the same amount in his account every week, w. What is the slope of the line? What does the slope represent in the context of the problem?

48. Desk 5 Pierce the plumber charges $25 for a service call
Desk 5 Pierce the plumber charges $25 for a service call. He use the equation C = 50h + 25 to determine the charge of his services, C, after working h hours. What is the slope of the line? What does the slope represent in the context of the problem?

49. Desk 6 Jose the plumber charges $65 per hour to fix your plumbing
Desk 6 Jose the plumber charges $65 per hour to fix your plumbing. He uses the equation C = 65h to determine the charge of his services, C, after working h hours. What is the y-intercept? What does it represent in the context of the problem?

50. Desk 7 Kristina is running the freshman class fundraiser
Desk 7 Kristina is running the freshman class fundraiser. They are selling key chains as a fundraiser. The amount of money they make is computed using the function y = 2x – 100, where x represents the number of key chains sold. What does the number 100 mean in the context of this problem?

51. Desk 8 Awa’s parents are saving to buy a new car for her 16th birthday
Desk 8 Awa’s parents are saving to buy a new car for her 16th birthday. The function y = 125x represents the relationship between the number of months her parents have been saving and the amount in their account. What does the number 3200 represent in the context of the problem?

52. Desk 9 Laura lights a candle in her kitchen
Desk 9 Laura lights a candle in her kitchen. The height of the candle is represented by the equation y = -½ x + 6, where x is the time in hours the candle has been burning and y is the height of the candle in inches. What was the height of the candle before Laura lit it?

53. Desk 10 Elizabeth has been paying her credit card bill since January 1st. The equation B = -100m represents the relationship between the time she has been paying, m, and the amount of her credit card bill, B. How much money did Elizabeth owe at the beginning of the year?

54. Desk 11 Aminata joins a CD club
Desk 11 Aminata joins a CD club. She pays $15 for the membership and $6 for each CD that she buys. Write an equation in slope-intercept form that models the relationship between the cost Aminata pays, y, and the number of CDs Aminata buys, x.

55. Desk 12 Kayla has $1500 in her bank account. She spends $150 each week
Desk 12 Kayla has $1500 in her bank account. She spends $150 each week. Write an equation that represents the relationship between the amount in Kayla’s bank account, A, and the number of weeks she has been spending, w

56. Desk 13 Ricardo is draining his pool for the winter
Desk 13 Ricardo is draining his pool for the winter. There are 240 gallons in the pool and it is decreasing at a rate of 20 gallons per hour. Write an equation to represent the relationship between the amount of water in the pool, y, and the number of hours the pool has been draining, x.

57. Desk 14
Airport DVD rentals is offering a new special for the busy holiday travel season. You can rent a portable DVD player and DVDs to take on your flight.
Write an equation to represent the relationship between the number of DVDs rented, d, and the total cost, c.

58. Desk 15
Mamma McGurkin is planning Thanksgiving dinner. The number of pounds of turkey she will buy depends on the number of people she invites to dinner.
Write an equation to represent the relationship between the number of people invited, x, and the number of pounds of turkey needed, y.

59. Desk 16 Kyle is training for a marathon. The equation y = 3x + 5
Desk 16 Kyle is training for a marathon. The equation y = 3x represents the number of miles Kyle can run over time, where y is the number of miles Kyle runs and x is the number of weeks Kyle has been training. How long will it take Kyle to be ready to run the entire marathon of 26.5 miles?

60. Desk 17 Priscilla begins working at Macy’s
Desk 17 Priscilla begins working at Macy’s. She will be paid a daily amount plus a commission of her total sales. The equation y = .10x + 15 represents the amount Priscilla will make based on her total sales, where y is the amount of money Priscilla makes in one day and x is her total sales. How much will Priscilla make if she sells $650?

61. Desk 18 David works at the T-shirt Shack selling tees
Desk 18 David works at the T-shirt Shack selling tees. The equation y = 15x – 520 represents the profit that the T-shirt Shack makes for each t-shirt sold, where y is the total profit and x is the number of t-shirts sold. How many t-shirts does the T-shirt Shack need to sell to make a profit of $140?

62. Desk 19 Alejandra paints faces at kids’ birthday parties to earn extra money. The equation M = 2.50f + 12 represents the relationship between the money she makes, M, and the number of faces she paints, f. Alejandra wants to buy a new pair of Uggs that cost $ How many faces does she need to paint?

63. Desk 20 Steven is learning to scuba dive
Desk 20 Steven is learning to scuba dive. The equation D = 20L + 15 represents the depth he can dive in feet, D, based on the number of lessons he has had, L. How deep can Steven dive after he takes 13 lessons?

64. Check Up!!! 2) 𝑦= 2 3 𝑥− 7 3 Identify the slope and the y-intercept.
1) 𝑦=−5𝑥+3 m= b=
Write an equation from the information given.
3) slope of -3 and y-intercept of 5
4) contains (0,7) and has a slope of -7
5) (-1,7) and (0,3)
6) (-7,2) and (5,-1)
2) 𝑦= 2 3 𝑥− 7 3 m= b=

65. Working in the book Page 557-558 (Problem 2) Page 564-565(Problem 1)

66. X-Intercepts
November 12th, 2014

67. Review all concepts
November 13th, 2014

68. Summative Assessment
November 14th, 2014