CO POWERPOINT MATH 5 LINE GRAPH edited final.pptx

A line graph—also known as a line plot or a line chart—is a graph that uses lines to connect individual data points. A line graph displays quantitative values over a specified time interval. In finance, line graphs are commonly used to depict the historical price action of an asset or security. In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G).

The name line graph comes from a paper by Harary & Norman (1960) although both Whitney (1932) and Krausz (1943) used the construction before this.[1] Other terms used for the line graph include the covering graph, the derivative, the edge-to-vertex dual, the conjugate, the representative graph, and the θ-obrazom,[1] as well as the edge graph, the interchange graph, the adjoint graph, and the derived graph.[2]

Hassler Whitney (1932) proved that with one exceptional case the structure of a connected graph G can be recovered completely from its line graph.[3] Many other properties of line graphs follow by translating the properties of the underlying graph from vertices into edges, and by Whitney's theorem the same translation can also be done in the other direction. Line graphs are claw-free, and the line graphs of bipartite graphs are perfect. Line graphs are characterized by nine forbidden subgraphs and can be recognized in linear time.

Various extensions of the concept of a line graph have been studied, including line graphs of line graphs, line graphs of multigraphs, line graphs of hypergraphs, and line graphs of weighted graphs. The line graph of a connected graph is connected. If G is connected, it contains a path connecting any two of its edges, which translates into a path in L(G) containing any two of the vertices of L(G). However, a graph G that has some isolated vertices, and is therefore disconnected, may nevertheless have a connected line graph.[5]
A line graph has an articulation point if and only if the underlying graph has a bridge for which neither endpoint has degree one.[2]
For a graph G with n vertices and m edges, the number of vertices of the line graph L(G) is m, and the number of edges of L(G) is half the sum of the squares of the degrees of the vertices in G, minus m.[6]
An independent set in L(G) corresponds to a matching in G. In particular, a maximum independent set in L(G) corresponds to maximum matching in G. Since maximum matchings may be found in polynomial time, so may the maximum independent sets of line graphs, despite the hardness of the maximum independent set problem for more general families of graphs.[4] Similarly, a rainbow-independent set in L(G) corresponds to a rainbow matching in G.
The edge chromatic number of a graph G is equal to the vertex chromatic numb

1. QURATER 4 LESSON IN MATH 6 Teacher: LEAH MAY DIANE M. CORPUZ

2. Rules to follow: Seat properly and avoid standing. Be sure that you have prepared the things needed for our lesson. 3. Be active in our class. 4. Listen to the directions. 5. Always wear your smile. 

3. Direction: Record the given temperature in degree Celsius (°C) .

4. 1. 40 °C

5. 2. 21 °C

6. 3. -30 °C

7. 4. 42 °C

8. 38.5 °C 5.

9. Let us play! “Happy Face or Sad Face”!

10. Direction: Show a happy face if the sentence is correct and sad face if not correct.

11. Word Puzzle   ____ ____ ____ ____ ____ ____ ____ ____ ____ 1 2 3 4 5 6 7 8 9

12. 1) The boiling point is 100°C.

13. Word Puzzle   ____ ____ ____ ____ ____ ____ ____ ____ ____ 1 2 3 4 5 6 7 8 9 I R

14. 2) Our normal body temperature is 32°C.

15. Word Puzzle   ____ ____ ____ ____ ____ ____ ____ ____ ____ 1 2 3 4 5 6 7 8 9 I R E A

16. 3) Temperature is the hotness or coldness of an object

17. Word Puzzle   ____ ____ ____ ____ ____ ____ ____ ____ ____ 1 2 3 4 5 6 7 8 9 I R E A G H

18. 4) The normal room temperature is 40°C .

19. Word Puzzle   ____ ____ ____ ____ ____ ____ ____ ____ ____ 1 2 3 4 5 6 7 8 9 I R E A G H N P

20. 5) Thermometer is the instrument used in measuring the temperature.

21. Word Puzzle   ____ ____ ____ ____ ____ ____ ____ ____ ____ 1 2 3 4 5 6 7 8 9 I R E A G H N P L

22. What is the word for today? This is our lesson, about LINE GRAPH

23. In time of pandemic, we need to stay at home for us to be safe. It is still not safe to go outside. There are still people being affected by COVID-19. Since we need to stay at home, how can we spend our time wisely?

24. The graph below shows the favorite hobbies of Grade five pupils during weekends especially in time of pandemic.

25. Direction : Use the data presented in the graph to answer these questions.

26. 1. What is the total number of pupils who like dancing and biking? 2. What is the average number of pupils in the first three least favorite hobbies?.

27. 3. How many more pupils like watching TV than gardening? 4. Based on the graph, why do you think playing computer games is the highest pupils’ hobby and gardening was the lowest?

28. 5. What do you think is the most enjoyable hobby? 6. Is it good for young children to use too much computer games? Why? What is the bad effect of too much use of gadget.

29. A line graph is a type of chart which shows information or value of something over a period of time. It has vertical (Y – axis) and horizontal (X –axis) which serve as guides in plotting the points for the lines.

30. These Y axis represents an increasing/ decreasing value of variables which may be money, scores, number of something . The X axis holds the end-lines of the line segment created by these variables relate to each other like people, animals, plants and things.

31. We use line graphs to compare trends of changes over a period of time for more than one group.  Read and analyze the problem. Aling Susan is a vendor. She wants to know the difference between the highest and lowest number of kilograms of fish sold on that day.

32. Let’s help Aling Susan to solve her problem by using the data in the line graph.   Using the line graph, you can determine the data which fish has the highest and lowest number of kilograms sold by Aling Susan.

33. Let’ s try now in solving the problem using data presented in the line graph above.   Question No 1 . - What is the difference between the highest number of kilograms and lowest number of kilograms of fish? 

34. 55 kg - highest number of kilograms – 30 kg – lowest number of kilograms 25 kg – difference between the highest and lowest number of kilograms

35. Question No. 2 - Based on the graph, why milkfish has the highest kilogram sold? To answer the question you are just making inferences . In making inference is just looking carefully at the facts and coming to conclusion . They are evidence- based guesses .

36. Let’s play! “Choose the Correct One!

37. Directions : Study the graph carefully and choose the letter of the correct answer.

38. 1. What is the title of the graph? A. Days B. Pesos C. Mang Ted’s Sari-Sari Store D. Average Daily Sale at Mang Ted’s Sari-Sari Store   D

39. 2. On what day does the store get the highest sale? A. Saturday B. Sunday C. Monday D. Tuesday   A

40. 3. On what days were the sales the same? A. Monday and Wednesday B. Friday and Sunday C. Friday and Tuesday D. Sunday and Tuesday   B

41. 4. How much was the total sales? A. P 3,350 B. P 3,400 C. P 3,450 D. P 3,500  

42. 4. How much was the total sales? A. P 3,350 B. P 3,400 C. P 3,450 D. P 3,500   C

43. 5. Which character trait does Mang Ted should need to possess to become a successful store owner? A. doubtful B. industrious C. lazy D. proud   B

44. Let’s have GROUP ACTIVITY!

45. 2. Karamihan sa mga kabataan ay nahuhumaling sa paglalaro gamit ang cellphone. A. Sila ay walang magawa sa bahay B. Walang kontrol sa paggamit ng cellphone C. Maraming pambili ng load D. Gusto lang gamitin ang cellphone Ano ang iyong sagot? Mahusay ! Titik B I will divide you into 4 groups. Each group will be given an activity to answer. Are you ready?

46. 2. Karamihan sa mga kabataan ay nahuhumaling sa paglalaro gamit ang cellphone. A. Sila ay walang magawa sa bahay B. Walang kontrol sa paggamit ng cellphone C. Maraming pambili ng load D. Gusto lang gamitin ang cellphone Ano ang iyong sagot? Mahusay ! Titik B Directions : Use the data in the line graph to answer the following questions. Group 1

47. 2. Karamihan sa mga kabataan ay nahuhumaling sa paglalaro gamit ang cellphone. A. Sila ay walang magawa sa bahay B. Walang kontrol sa paggamit ng cellphone C. Maraming pambili ng load D. Gusto lang gamitin ang cellphone Ano ang iyong sagot? Mahusay ! Titik B

48. 2. Karamihan sa mga kabataan ay nahuhumaling sa paglalaro gamit ang cellphone. A. Sila ay walang magawa sa bahay B. Walang kontrol sa paggamit ng cellphone C. Maraming pambili ng load D. Gusto lang gamitin ang cellphone Ano ang iyong sagot? Mahusay ! Titik B 1. In which day /s were Anton’s expenses is less than Eli’s? 2. What is the difference between their expenses on Friday? 3. What is the average expenses of Anton for a week? 4. Between which two days did Anton’s and Eli’s expenses increase the most? 5. Who has fewer expenses between the two?

49. 2. Karamihan sa mga kabataan ay nahuhumaling sa paglalaro gamit ang cellphone. A. Sila ay walang magawa sa bahay B. Walang kontrol sa paggamit ng cellphone C. Maraming pambili ng load D. Gusto lang gamitin ang cellphone Ano ang iyong sagot? Mahusay ! Titik B Directions : Use the data in the line graph to answer the following questions. Group 2

50. 2. Karamihan sa mga kabataan ay nahuhumaling sa paglalaro gamit ang cellphone. A. Sila ay walang magawa sa bahay B. Walang kontrol sa paggamit ng cellphone C. Maraming pambili ng load D. Gusto lang gamitin ang cellphone Ano ang iyong sagot? Mahusay ! Titik B

51. 2. Karamihan sa mga kabataan ay nahuhumaling sa paglalaro gamit ang cellphone. A. Sila ay walang magawa sa bahay B. Walang kontrol sa paggamit ng cellphone C. Maraming pambili ng load D. Gusto lang gamitin ang cellphone Ano ang iyong sagot? Mahusay ! Titik B 1. How much farther does Mabel walk than Jenny? 2. How much lesser does Jenny walk than Joan? 3. What is the difference between Nora’s walk and Mabel ’s walk in meters? 4. What is the combined distance walked by the Zumba members? 5. Give the advantage of Zumba workout in our body.

52. 2. Karamihan sa mga kabataan ay nahuhumaling sa paglalaro gamit ang cellphone. A. Sila ay walang magawa sa bahay B. Walang kontrol sa paggamit ng cellphone C. Maraming pambili ng load D. Gusto lang gamitin ang cellphone Ano ang iyong sagot? Mahusay ! Titik B Directions : Use the data in the line graph to answer the following questions. Group 3

53. 2. Karamihan sa mga kabataan ay nahuhumaling sa paglalaro gamit ang cellphone. A. Sila ay walang magawa sa bahay B. Walang kontrol sa paggamit ng cellphone C. Maraming pambili ng load D. Gusto lang gamitin ang cellphone Ano ang iyong sagot? Mahusay ! Titik B

54. 2. Karamihan sa mga kabataan ay nahuhumaling sa paglalaro gamit ang cellphone. A. Sila ay walang magawa sa bahay B. Walang kontrol sa paggamit ng cellphone C. Maraming pambili ng load D. Gusto lang gamitin ang cellphone Ano ang iyong sagot? Mahusay ! Titik B 1. What is the total number of visitors go to Jed’s Island and Eight Waves during summer? 2. What is the difference between the highest and lowest visited resort in B ulacan? 3. What was the average number of visitors visited in the different resorts in Bulacan? 4. Give inference why Amana Water Park was the most number of visitors among the resort. 5. Compare the number of visitors in Hidden Sanctuary and Eight Waves.

55. 2. Karamihan sa mga kabataan ay nahuhumaling sa paglalaro gamit ang cellphone. A. Sila ay walang magawa sa bahay B. Walang kontrol sa paggamit ng cellphone C. Maraming pambili ng load D. Gusto lang gamitin ang cellphone Ano ang iyong sagot? Mahusay ! Titik B Directions : Use the data in the line graph to answer the following questions. Group 4

56. 2. Karamihan sa mga kabataan ay nahuhumaling sa paglalaro gamit ang cellphone. A. Sila ay walang magawa sa bahay B. Walang kontrol sa paggamit ng cellphone C. Maraming pambili ng load D. Gusto lang gamitin ang cellphone Ano ang iyong sagot? Mahusay ! Titik B

57. 2. Karamihan sa mga kabataan ay nahuhumaling sa paglalaro gamit ang cellphone. A. Sila ay walang magawa sa bahay B. Walang kontrol sa paggamit ng cellphone C. Maraming pambili ng load D. Gusto lang gamitin ang cellphone Ano ang iyong sagot? Mahusay ! Titik B 1. In what months have the same temperature in Malolos City? 2. What is the total temperature of the top three hottest months in Malolos City? 3. How many degrees is the difference between the highest and lowest temperature in Baguio City? 4. Why do you think that Baguio City has the lowest temperature compare to Malolos City? 5. What is the possible cause of high and low temperature?

58. Let’s Apply What Have you Learned!

59. Directions : Use the line graph to answer the questions .Write your answer inside the figures.

60. 1. What is the sum of pupils using computers in studying during Monday and Friday?

61. 2. Compute the average number of pupils who used computers in studying during the first four consecutive days.

62. 3. What is the total of pupils using computers in studying during weekends?

63. 4. What is the highest recorded number of pupils using computers in studying?

64. 5. Based on the graph, what is the most preferred day of the pupils in using computers for their studies?

65. Remember: In time of pandemic, we need to stay in our home; we must spend our time in a worthwhile manner. We can have different hobbies like planting or gardening. Avoid too much use of gadgets because it is not good for our health.

66. Let’s Summarize!

67. Line Graph - is useful in displaying data or information as a series of data points called markers connected by straight line segments. Ideas to Remember:

68. Double Line Graph - A double line graph used to show the comparison of two data. Draw Inference - is just looking carefully at the facts and coming to conclusion. They are evidence-based guesses. Ideas to Remember:

69. EVALUATION

70. Directions: Use the line graph to answer the given questions. Encircle the letter of the correct answer.  

71. 1. How many minutes did Michelle exercise during Monday and Tuesday? A. 110 minutes B. 120 minutes C. 130 minutes D. 140 minutes

72. 2. What day with the least minutes when Michelle exercised? A. Monday B. Tuesday C. Wednesday D. Thursday

73. 3. What is the average number of minutes Michelle spent in exercising? A. 52 minutes B. 53 minutes C. 54 minutes D. 55 minutes

74. 4. How much time did Michelle exercise for the first three consecutive days? A. 135 minutes B. 140 minutes C. 145 minutes D. 150 minutes

75. 5. 5. Which of the following could be the best reason why Tuesday had the most time spent by Michelle in exercising? A. day off B. on duty C. hectic day D. working day

76. Assignment:

77. Directions : Analyze the line graph and answer the following questions. Write your answer in your notebook.

78. 1. What is the total number of pupils who likes cat? 2. What is the difference between the highest and lowest number of favorite pets at home? 3. What was the average number of pupil’s favorite pets at home? 4. Give inference why dog was the most number of pupils favorite pets at home. 5. What is the title of the graph?