LaynaMae 2 years ago Help?

1. LaynaMae

2. ganeshie8

average rate of change = change in y / change in x

3. ganeshie8

you're going from x=3 to x=5 so, chang ein x = 5-3 = 2

4. ganeshie8

do u knw how to find change in y, from the given table ?

5. LaynaMae

But what about the 1 ?

6. LaynaMae

And no , all of this is confusing to me :(

7. ganeshie8

its okay to get confuse when u start... did u get how we got the change in x ?

8. LaynaMae

Yes, we subtracted them? :o

9. ganeshie8

yes, now look at table. and tell me wats the y value, when x = 5 and when x = 3

10. LaynaMae

When x=5 , the y value is -2 . When x=3 , the y value is 4

11. ganeshie8

excellent ! so change in y = -2-4 = -6

12. ganeshie8

average rate of change = change in y / change in x = -6/2 = -3

13. ganeshie8

see if that makes sense

14. LaynaMae

That does makes sense ! :D

15. ganeshie8

cool :)

16. LaynaMae

Thank you so much, I have a few more questions? Would you be willing to help?

17. ganeshie8

18. LaynaMae

I will attach it as a picture so it will be easier :)

19. ganeshie8

find m, the rate of change of first

20. ganeshie8

(-1, 3) and (1 , 7)

21. ganeshie8

those are the given points

22. ganeshie8

(-1, 3) and (1 , 7) x1 y1 x2 y2

23. ganeshie8

rate of change , m = change in y / change in x = y2-y1 / x2-x1

24. ganeshie8

= 7-3 / 1--1 = 4/2 =2 so, m = 2

25. LaynaMae

Right :) I'm working it out on paper with you :P

26. ganeshie8

now, use this :- equation of line in slope, point form is, y - y1 = m(x-x1) plugin values :)

27. LaynaMae

That would be y - 3 = 2 (x - (-1)) ?

28. ganeshie8

Yes !

29. LaynaMae

Yay !!

30. LaynaMae

So is that it ? :o

31. ganeshie8

not yet, thats one equation. we could have used the second point aswell... let me do it for you :)

32. LaynaMae

Oh , okay :) Thank you !

33. ganeshie8

slope m = 2, second point (1 , 7) so m = 2, x1 = 1, y1=7 y-y1 = m(x-x1) plugin values now

34. ganeshie8

y-7 = 2(x-1)

35. ganeshie8

thats the second equation. now see which one exists in the given options , and tick that one...

36. LaynaMae

It's option 2 ! :)

37. LaynaMae

You helped me understand this ! Thank you :D

38. ganeshie8

Yes ! takes time to master these... i see you're already getting good at these :)

39. LaynaMae

I have 3 more questions left and 2 are easy , once I answer those may you help me with the very last question ?? Pleasee :p

40. ganeshie8

np, i hav time :)

41. ganeshie8

just holler when u r done wid the two prblms... ;)

42. LaynaMae

Haha okay !! :)

43. LaynaMae

Okay here's the last question :) Jack and Jill had 3 pails of water. Each trip up the hill, Jack and Jill obtained 1 more bucket of water. Which of the graphs below represents Jack and Jill's number of pails over time?

44. ganeshie8

check ur 3rd & 4th graphs. they are same !

45. LaynaMae

That's how it is on my quiz :( It's probably an error ... Is there anyway to do this and figure out the answer and see if it's on one of the graphs ? If not , I don't think my teacher will deduct points for the question being incorrect lol

46. ganeshie8

ohk, but wat wud u pick whe u have two exact same graphs ?

47. LaynaMae

Ugh I'm just going to chose an answer and tell my teacher there was an error with the questions . Thank you though :)

48. ganeshie8

good :) here is how we solve it :- since to start with, they have 3 pails of water, that means, the line must cit the y- axis at 3

49. ganeshie8

since the line is cutting y-axis at 3 only in 3rd & 4th graphs, one of them must be ur answer

50. ganeshie8

and since, both graphs are exact same, u toss a coin and pick one

51. LaynaMae

Haha okay :) Thank you so much for your help :)

52. ganeshie8

np :) goodluck wid ur assignment :)

53. LaynaMae

WAITTT ! This one ?? :o

54. LaynaMae

Can you help ? :o

55. ganeshie8

ha, take first equation, and solve x

56. ganeshie8

first equaiton :- 2x+4 = 3x-11

57. ganeshie8

can you solve x ?

58. LaynaMae

Yes, give me a minute :)

59. ganeshie8

take ur time =)

60. LaynaMae

61. LaynaMae

Second one is 16

62. LaynaMae

I need help solving the last one ...

63. ganeshie8

second one is 16 $$\checkmark$$

64. ganeshie8

but first one is not 3

65. LaynaMae

It's not ? :( What's the first one ?

66. ganeshie8

2x+4 = 3x-11 subtract 2x both sides 4 = x - 11 add 11 both sides 15 = x

67. ganeshie8

first one is 15

68. LaynaMae

Ohhhhh ! I know what I did wrong ! I added 3x and 2x by mistake ! haha

69. ganeshie8

:) i thought so... third equation :- $$\large \frac{2x+1}{3} = \frac{x+6}{2}$$

70. ganeshie8

cross multiply

71. LaynaMae

How would I start ? :( I'm no good in cross multiplying ..

72. ganeshie8

$$\large \frac{2x+1}{3} = \frac{x+6}{2}$$ $$\large 2(2x+1) = 3(x+6)$$

73. LaynaMae

Omg that makes sense -.- ! Okay I understand now !

74. ganeshie8

cool :) solve x

75. ganeshie8

$$\large \frac{2x+1}{3} = \frac{x+6}{2}$$ $$\large 2(2x+1) = 3(x+6)$$ $$\large 4x+2 = 3x+18$$ solve x

76. LaynaMae

4x + 2 = 3x + 18 ? Then solve ?

77. ganeshie8

yes !

78. LaynaMae

Okay one moment !

79. ganeshie8

oki

80. LaynaMae

Is x = -16 ?

81. ganeshie8

$$\large \frac{2x+1}{3} = \frac{x+6}{2}$$ $$\large 2(2x+1) = 3(x+6)$$ $$\large 4x+2 = 3x+18$$ subtract 3x both sides $$\large x+2 = 18$$

82. ganeshie8

that gives, x = ?

83. LaynaMae

Oh sorry I subtracted 4x by mistake !

84. ganeshie8

ok.. x = ?

85. LaynaMae

One sec

86. ganeshie8

$$\large \frac{2x+1}{3} = \frac{x+6}{2}$$ $$\large 2(2x+1) = 3(x+6)$$ $$\large 4x+2 = 3x+18$$ subtract 3x both sides $$\large x+2 = 18$$ subtract 2 both sides $$\large x = 16$$

87. LaynaMae

Should be 16 !

88. ganeshie8

x = 16 ! :)

89. LaynaMae

Yay :D

90. LaynaMae

So equations 1 and 3 have the same solution !

91. ganeshie8

yes ! so we got, first one, x = 15 second one, x = 16 third one, x = 16

92. ganeshie8

careful madam, equations 2 and 3 have the same solution

93. LaynaMae

THANK YOU THANK YOU THANK YOU !! :) & yes I got confused haha but now i get it :)

94. ganeshie8

glad to hear that :) you're wlcme !!

95. LaynaMae

Are you willing to help me out with 4 more questions ? And that it for the day !! Haha