## MasuKasu Group Title I haven't done Algebra in over 5 years, so I need help with this problem: What’s the equation of a line that passes through points (0, -1) and (2, 3)? one year ago one year ago

1. bettyboop8904 Group Title

First to find the slope of the line you use the equation: $\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }$ pick one of the pairs to plug into $y _{2}$ and $x _{2}$ just make sure to keep the order after you start plugging numbers in. Does this make sense so far?

2. bettyboop8904 Group Title

you want to obtain y=mx+b and that formula is the formula for slope (aka "m") @masukasu

3. MasuKasu Group Title

How do I know what numbers to assign to y and x?

4. bettyboop8904 Group Title

so this is what it will look like once you plug the points in: $\frac{ (3) - (-1) }{ (2)-(0) }$

5. bettyboop8904 Group Title

You have the points (0, -1) and (2, 3); you know that 0 and 2 are x-values and -1 and 3 are y-values, correct?

6. bettyboop8904 Group Title

I used the second set of points to use first only so the equation won't look messy. Putting the -1 in the $y _{1}$ spot allows it to become positive because two negatives make a positive.

7. MasuKasu Group Title

So, (0, -1) and (2, 3) would look like this with their appropriate values: (x, -y) and (x, y) right?

8. bettyboop8904 Group Title

But you will get the same answer no matter which set of points you plug first, but always be sure to keep the order and correct to your above question

9. bettyboop8904 Group Title

so go ahead and solve for the slope (m) and tell me what you get

10. MasuKasu Group Title

But, the example of the order of my values(in my last comment) are correct, right?

11. bettyboop8904 Group Title

yes you are correct = )

12. MasuKasu Group Title

Ah! Thank you. I'll try to solve the problem. One minute (:

13. bettyboop8904 Group Title

now that is only part of it, there is another equation to arrive to the final equation

14. bettyboop8904 Group Title

once you find the slope I can tell you the next part = )

15. MasuKasu Group Title

And I would multiply $x{2}$ and $y{2}$ like any other number with power, right? i.e. 2 x 2 and 3 x 3

16. bettyboop8904 Group Title

Oh I'm sorry, the subscript 1 and 2 are only there to decipher between the different values those aren't exponents

17. MasuKasu Group Title

Ohhh ok, thank you. I couldn't remember the right terminology either, sorry. But, I think it's: $\frac{ 4 }{ -1 }$

18. bettyboop8904 Group Title

here let me do this $\frac{ y-y }{ x-x }$ do you see how this can look like the answer would be 0 right? that's why they put the 1 and 2 on the x and y to determine between the two sets of points

19. bettyboop8904 Group Title

20. MasuKasu Group Title

Pff... Sorry. I mixed my numbers up >.<

21. bettyboop8904 Group Title

no apologies = ) I was just on here earlier getting help and I did the same thing lol ; D

22. MasuKasu Group Title

Essentially it comes out to $\frac{ 2 }{ 1 }$

23. MasuKasu Group Title

lol I guess we all make mistakes haha! It's how we learn.

24. bettyboop8904 Group Title

correct = ) so that is your "m" or slope

25. MasuKasu Group Title

yay! Alright, so that should be written out like so: $y =2x +b$

26. MasuKasu Group Title

And b is the 'base', right?

27. bettyboop8904 Group Title

the next equation you will need is: $y-y _{1} = m (x-x _{1})$ Now don't get confused that the $y _{1}$ and $x _{1}$ are the same as the ones above you can choose either set of points to plug in. The regular y and x are the ones that will remain in the equation after plugging in the set of points which will give you the y=mx+b. Does this make sense so far?

28. bettyboop8904 Group Title

I can't remember if it is called the base but that will be your y-intercept once you graph it

29. bettyboop8904 Group Title

Ok so i chose the points (2,3) to use bc I like positive numbers lol Plug in the set of points and what you got for m into the equation $y-(3)=(2)(x-(2))$ Tell me what you get after solving that

30. bettyboop8904 Group Title

@masukasu

31. MasuKasu Group Title

Sorry. Someone had to use my laptop.

32. bettyboop8904 Group Title

that's ok = )

33. MasuKasu Group Title

Ok, I'm going to solve that. One minute (:

34. MasuKasu Group Title

Wait... Do I NEED the parenthesis around the numbers? Or does it not really change anything?

35. bettyboop8904 Group Title

It's just easier to see if you have any sign changes. Now say you used the other set of points instead of the positive numbers you would end up with this: $y-(-1) = (2)(x-0)$ It's safe to have that parentheses around the -1 bc the sign of it changes to y+1 which will screw things up when you have to solve for y

36. bettyboop8904 Group Title

but it will only screw things up when you have to solve for y if you forget to change the sign of the -1.

37. MasuKasu Group Title

This equation is a little confusing. I'm used to it looking like $2\left( x -2 \right)=y -\left( 3 \right)$ but even then, it's a little difficult.

38. bettyboop8904 Group Title

ok so the only difference is the sides of the equation are on opposite sides = ) do you know how to factor? I'll help you step by step = )

39. MasuKasu Group Title

I would bring the 3 over and it would become a +3, then it would look like this:$2\left( x-2 \right)+3=y$ I think

40. MasuKasu Group Title

Factoring... Uh lol Is that factoring? I can't remember. Am I able to reverse the equation like I did though?

41. bettyboop8904 Group Title

that is a correct move but that's not factoring. Take a look at the 2(x-2): when you see something like this you use factoring where you take the front number and multiply it by both numbers inside the parentheses. So you would have 2*x - 4 then tack on what's left in the equation: 2x-4+3=y Then simplify

42. MasuKasu Group Title

OH! I remember now!

43. MasuKasu Group Title

Well... that part at least

44. bettyboop8904 Group Title

|dw:1359321905435:dw|

45. MasuKasu Group Title

And then that would turn into $y =2x-12$ right?

46. MasuKasu Group Title

No wait.... Ugh! I think that's wrong actually.

47. MasuKasu Group Title

lol Yeah, I loved the Illustration haha!

48. bettyboop8904 Group Title

no look at it this way: $y= 2x+(-4) +3$ $y=2x +(-1)$ $y=2x-1$ Does that make sense? = D

49. MasuKasu Group Title

|dw:1359322373754:dw|

50. MasuKasu Group Title

Trying to rework the problem so I can better understand it...

51. MasuKasu Group Title

(2 x X)=2x (2 x 2)=4 y=2x ???????????? I can't figure out how you got the -4

52. bettyboop8904 Group Title

I'm sorry I keep doing it backwards from what you are used to = ( I have my blonde moments lol I'm going to draw it for you and instead try not moving the 3 as the first move

53. MasuKasu Group Title

I uh.... Well, I have blonde moments too lol And I've black hair and I'm Asian haha! So, no worries :P

54. bettyboop8904 Group Title

I'm a brunette lmfao

55. MasuKasu Group Title

It's the 2x+(-4) part that gets me

56. MasuKasu Group Title

lawl xD

57. bettyboop8904 Group Title

|dw:1359322879897:dw|

58. bettyboop8904 Group Title

this is the way you're used to right?

59. MasuKasu Group Title

Yeah

60. bettyboop8904 Group Title

ok here we go lol

61. bettyboop8904 Group Title

|dw:1359322994943:dw|

62. bettyboop8904 Group Title

|dw:1359323398039:dw|

63. MasuKasu Group Title

Hopefully I can get this done before I have to go to work xD I have a history in high school of a single math problem taking me almost 2-3 hours to figure out.

64. bettyboop8904 Group Title

it's always good to make an equation have positives so y-(+3) can also be written as y+(-3) its the same thing

65. MasuKasu Group Title

Trying to understand this... I always had a hard time understanding these problems because of all the positives switching to negatives and vice versa.

66. bettyboop8904 Group Title

so back to the full equation and i'll make it fast = ) a lot of people have problems with this that's why I'm here to help although my explanations seem long at times lol I apologize = )

67. MasuKasu Group Title

Ohhh so that's what you did +(-4), right?

68. bettyboop8904 Group Title

Ok so we have: |dw:1359323569725:dw||dw:1359323806202:dw|

69. bettyboop8904 Group Title

yes correct! = D

70. MasuKasu Group Title

$y=2x + \left( -4+3 \right)$ right? Which becomes $y =2x$ With the +(-4), that + sign pretty much comes out of nowhere, right?

71. MasuKasu Group Title

Correction: $y =2x +1$ Sorry

72. bettyboop8904 Group Title

lol yeah pretty much. that's what I've been learning as I've gotten through to later math classes [calculus 2 now = ( lol] is that you can just put random stuff in an equation that isn't even in it just as long as it doesn't change the equation haha and yes you are correct I think you got it = D So do you understand it now?

73. bettyboop8904 Group Title

Do you feel confident that you can do another one by yourself?

74. MasuKasu Group Title

I would like to try (: So, shoot! Let's see if I can do this.

75. bettyboop8904 Group Title

ok let me just quickly work one out to make sure its not messy lol like no fractions i hate fractions lol

76. MasuKasu Group Title

And I had to repeat Pre-Algebra once, went on to Algebra 1, and didn't do too well there.

77. MasuKasu Group Title

Ok! And you're 50,000,000 times smarter than me haha!

78. MasuKasu Group Title

While you're doing that, I'm going to take a super fast shower. Like... 5-10 minutes.

79. bettyboop8904 Group Title

ok when you get back I will have the equation already up = )

80. MasuKasu Group Title

Ok (: Be back soon!

81. bettyboop8904 Group Title

What is the equation of a line that passes through points (-1,6) and (3,-2)?

82. MasuKasu Group Title

Back! I'll figure that out real quick.

83. bettyboop8904 Group Title

kk = )

84. MasuKasu Group Title

So, I want to figure out y+mx+b right?

85. MasuKasu Group Title

Correction: y=mx+b

86. bettyboop8904 Group Title

correct and you will use two formulas to figure that out: $\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }$ $m(x-x _{1})=y-y _{1}$

87. bettyboop8904 Group Title

correction: $m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }$

88. MasuKasu Group Title

Ok, so does that second formula come from somewhere or do you have to remember it? lol

89. bettyboop8904 Group Title

you have to remember those

90. MasuKasu Group Title

Sorry. Does it come from somewhere within the first formula, or does it come from nowhere, except memory?

91. bettyboop8904 Group Title

it sucks bc there is so much memorization in math = (

92. MasuKasu Group Title

Yeahhhhh lol >.<

93. bettyboop8904 Group Title

just memory bc they give you the formula in class

94. MasuKasu Group Title

Uhhhhhhhhhhhhhhhhhhhhhhhhhh..... Ok here goes >.<$y =2x -1$

95. bettyboop8904 Group Title

no but good try let's go through it step by step. I admit it's a little challenging with all the sign changes

96. bettyboop8904 Group Title

what did you get for the slope?

97. MasuKasu Group Title

Where's my Fail Whale when I need it? xD

98. bettyboop8904 Group Title

= )

99. MasuKasu Group Title

m=2

100. bettyboop8904 Group Title

ok that's probably where it went wrong

101. bettyboop8904 Group Title

so how did you set it up? which set of points did you put first?

102. MasuKasu Group Title

We have to be fast though. I have to leave for work in 15 minutes o.o

103. bettyboop8904 Group Title

I'll be sure of it = )

104. MasuKasu Group Title

This is hard. One sec.

105. MasuKasu Group Title

|dw:1359326845829:dw|

106. MasuKasu Group Title

|dw:1359326969637:dw|

107. bettyboop8904 Group Title

I see what you did you put the values in the wrong locations

108. MasuKasu Group Title

Ahhhhhhhhhhhhhhhh! I feel dumb haha! Help me with that please?

109. bettyboop8904 Group Title

ok you have the points: (-1,6) and (3,-2) |dw:1359327131329:dw|

110. bettyboop8904 Group Title

that's supposed to be a 2 at the end of that second y (subscript)

111. MasuKasu Group Title

Oops.... Blonde moment? Or just blind? xD

112. bettyboop8904 Group Title

|dw:1359327213071:dw|

113. bettyboop8904 Group Title

y1 and x1 are the same set is what that says lol like I said we all have 'em lol

114. bettyboop8904 Group Title

what i usually do is when I'm given the two sets of points I label the numbers so I don't get confused later in the problem

115. bettyboop8904 Group Title

just as I did here |dw:1359327396584:dw|

116. MasuKasu Group Title

I did that too lol

117. bettyboop8904 Group Title

Did you re-work it out?

118. bettyboop8904 Group Title

If you have to leave for work I'll post how to do the full equation and the answer at the end = )

119. MasuKasu Group Title

One sec. I wish they'd call in so I could study more for the ASVAB :( I'll try to figure it out real quick

120. bettyboop8904 Group Title

lol kk = )

121. MasuKasu Group Title

m=-2

122. MasuKasu Group Title

Ya? lol

123. bettyboop8904 Group Title

yes! = D

124. MasuKasu Group Title

YES! Ok, let me solve the rest ;D

125. bettyboop8904 Group Title

lol kk

126. MasuKasu Group Title

Or try haha! I hope this is right.

127. bettyboop8904 Group Title

I'm sure you got it = )

128. MasuKasu Group Title

I uh.... I'm doubtful, but here goes o.o y=-2x-5 -_-

129. bettyboop8904 Group Title

very extremely close which points did you plug in?

130. MasuKasu Group Title

OH! When I brought over the -6, I left it as -6 and didn't switch it to 6

131. MasuKasu Group Title

y=2x+7 ??????????????????

132. bettyboop8904 Group Title

take a deep breath you're using (-1,6) right?

133. bettyboop8904 Group Title

= )

134. MasuKasu Group Title

Yeah I am lol

135. bettyboop8904 Group Title

|dw:1359328160642:dw|

136. bettyboop8904 Group Title

$-2x+4=y$

137. bettyboop8904 Group Title

Have a good day at work = )

138. MasuKasu Group Title

SORRY! My laptop actually overheated. I was also kind of late to work ^^;