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MasuKasu

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

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  1. bettyboop8904
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    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?

    • one year ago
  2. bettyboop8904
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    you want to obtain y=mx+b and that formula is the formula for slope (aka "m") @masukasu

    • one year ago
  3. MasuKasu
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    How do I know what numbers to assign to y and x?

    • one year ago
  4. bettyboop8904
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    so this is what it will look like once you plug the points in: \[\frac{ (3) - (-1) }{ (2)-(0) }\]

    • one year ago
  5. bettyboop8904
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    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?

    • one year ago
  6. bettyboop8904
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    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.

    • one year ago
  7. MasuKasu
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    So, (0, -1) and (2, 3) would look like this with their appropriate values: (x, -y) and (x, y) right?

    • one year ago
  8. bettyboop8904
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    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

    • one year ago
  9. bettyboop8904
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    so go ahead and solve for the slope (m) and tell me what you get

    • one year ago
  10. MasuKasu
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    But, the example of the order of my values(in my last comment) are correct, right?

    • one year ago
  11. bettyboop8904
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    yes you are correct = )

    • one year ago
  12. MasuKasu
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    Ah! Thank you. I'll try to solve the problem. One minute (:

    • one year ago
  13. bettyboop8904
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    now that is only part of it, there is another equation to arrive to the final equation

    • one year ago
  14. bettyboop8904
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    once you find the slope I can tell you the next part = )

    • one year ago
  15. MasuKasu
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    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

    • one year ago
  16. bettyboop8904
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    Oh I'm sorry, the subscript 1 and 2 are only there to decipher between the different values those aren't exponents

    • one year ago
  17. MasuKasu
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    Ohhh ok, thank you. I couldn't remember the right terminology either, sorry. But, I think it's: \[\frac{ 4 }{ -1 }\]

    • one year ago
  18. bettyboop8904
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    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

    • one year ago
  19. bettyboop8904
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    your numerator is correct double check your denominator (2-0) = ?

    • one year ago
  20. MasuKasu
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    Pff... Sorry. I mixed my numbers up >.<

    • one year ago
  21. bettyboop8904
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    no apologies = ) I was just on here earlier getting help and I did the same thing lol ; D

    • one year ago
  22. MasuKasu
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    Essentially it comes out to \[\frac{ 2 }{ 1 }\]

    • one year ago
  23. MasuKasu
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    lol I guess we all make mistakes haha! It's how we learn.

    • one year ago
  24. bettyboop8904
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    correct = ) so that is your "m" or slope

    • one year ago
  25. MasuKasu
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    yay! Alright, so that should be written out like so: \[y =2x +b\]

    • one year ago
  26. MasuKasu
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    And b is the 'base', right?

    • one year ago
  27. bettyboop8904
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    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?

    • one year ago
  28. bettyboop8904
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    I can't remember if it is called the base but that will be your y-intercept once you graph it

    • one year ago
  29. bettyboop8904
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    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

    • one year ago
  30. bettyboop8904
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    @masukasu

    • one year ago
  31. MasuKasu
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    Sorry. Someone had to use my laptop.

    • one year ago
  32. bettyboop8904
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    that's ok = )

    • one year ago
  33. MasuKasu
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    Ok, I'm going to solve that. One minute (:

    • one year ago
  34. MasuKasu
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    Wait... Do I NEED the parenthesis around the numbers? Or does it not really change anything?

    • one year ago
  35. bettyboop8904
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    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

    • one year ago
  36. bettyboop8904
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    but it will only screw things up when you have to solve for y if you forget to change the sign of the -1.

    • one year ago
  37. MasuKasu
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    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.

    • one year ago
  38. bettyboop8904
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    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 = )

    • one year ago
  39. MasuKasu
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    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

    • one year ago
  40. MasuKasu
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    Factoring... Uh lol Is that factoring? I can't remember. Am I able to reverse the equation like I did though?

    • one year ago
  41. bettyboop8904
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    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

    • one year ago
  42. MasuKasu
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    OH! I remember now!

    • one year ago
  43. MasuKasu
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    Well... that part at least

    • one year ago
  44. bettyboop8904
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    |dw:1359321905435:dw|

    • one year ago
  45. MasuKasu
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    And then that would turn into \[y =2x-12\] right?

    • one year ago
  46. MasuKasu
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    No wait.... Ugh! I think that's wrong actually.

    • one year ago
  47. MasuKasu
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    lol Yeah, I loved the Illustration haha!

    • one year ago
  48. bettyboop8904
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    no look at it this way: \[y= 2x+(-4) +3\] \[y=2x +(-1) \] \[y=2x-1\] Does that make sense? = D

    • one year ago
  49. MasuKasu
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    |dw:1359322373754:dw|

    • one year ago
  50. MasuKasu
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    Trying to rework the problem so I can better understand it...

    • one year ago
  51. MasuKasu
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    (2 x X)=2x (2 x 2)=4 y=2x ???????????? I can't figure out how you got the -4

    • one year ago
  52. bettyboop8904
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    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

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

    • one year ago
  54. bettyboop8904
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    I'm a brunette lmfao

    • one year ago
  55. MasuKasu
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    It's the 2x+(-4) part that gets me

    • one year ago
  56. MasuKasu
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    lawl xD

    • one year ago
  57. bettyboop8904
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    |dw:1359322879897:dw|

    • one year ago
  58. bettyboop8904
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    this is the way you're used to right?

    • one year ago
  59. MasuKasu
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    Yeah

    • one year ago
  60. bettyboop8904
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    ok here we go lol

    • one year ago
  61. bettyboop8904
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    |dw:1359322994943:dw|

    • one year ago
  62. bettyboop8904
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    |dw:1359323398039:dw|

    • one year ago
  63. MasuKasu
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    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.

    • one year ago
  64. bettyboop8904
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    it's always good to make an equation have positives so y-(+3) can also be written as y+(-3) its the same thing

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

    • one year ago
  66. bettyboop8904
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    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 = )

    • one year ago
  67. MasuKasu
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    Ohhh so that's what you did +(-4), right?

    • one year ago
  68. bettyboop8904
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    Ok so we have: |dw:1359323569725:dw||dw:1359323806202:dw|

    • one year ago
  69. bettyboop8904
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    yes correct! = D

    • one year ago
  70. MasuKasu
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    \[y=2x + \left( -4+3 \right)\] right? Which becomes \[y =2x\] With the +(-4), that + sign pretty much comes out of nowhere, right?

    • one year ago
  71. MasuKasu
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    Correction: \[y =2x +1\] Sorry

    • one year ago
  72. bettyboop8904
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    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?

    • one year ago
  73. bettyboop8904
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    Do you feel confident that you can do another one by yourself?

    • one year ago
  74. MasuKasu
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    I would like to try (: So, shoot! Let's see if I can do this.

    • one year ago
  75. bettyboop8904
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    ok let me just quickly work one out to make sure its not messy lol like no fractions i hate fractions lol

    • one year ago
  76. MasuKasu
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    And I had to repeat Pre-Algebra once, went on to Algebra 1, and didn't do too well there.

    • one year ago
  77. MasuKasu
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    Ok! And you're 50,000,000 times smarter than me haha!

    • one year ago
  78. MasuKasu
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    While you're doing that, I'm going to take a super fast shower. Like... 5-10 minutes.

    • one year ago
  79. bettyboop8904
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    ok when you get back I will have the equation already up = )

    • one year ago
  80. MasuKasu
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    Ok (: Be back soon!

    • one year ago
  81. bettyboop8904
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    What is the equation of a line that passes through points (-1,6) and (3,-2)?

    • one year ago
  82. MasuKasu
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    Back! I'll figure that out real quick.

    • one year ago
  83. bettyboop8904
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    kk = )

    • one year ago
  84. MasuKasu
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    So, I want to figure out y+mx+b right?

    • one year ago
  85. MasuKasu
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    Correction: y=mx+b

    • one year ago
  86. bettyboop8904
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    correct and you will use two formulas to figure that out: \[\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\] \[m(x-x _{1})=y-y _{1}\]

    • one year ago
  87. bettyboop8904
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    correction: \[m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]

    • one year ago
  88. MasuKasu
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    Ok, so does that second formula come from somewhere or do you have to remember it? lol

    • one year ago
  89. bettyboop8904
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    you have to remember those

    • one year ago
  90. MasuKasu
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    Sorry. Does it come from somewhere within the first formula, or does it come from nowhere, except memory?

    • one year ago
  91. bettyboop8904
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    it sucks bc there is so much memorization in math = (

    • one year ago
  92. MasuKasu
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    Yeahhhhh lol >.<

    • one year ago
  93. bettyboop8904
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    just memory bc they give you the formula in class

    • one year ago
  94. MasuKasu
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    Uhhhhhhhhhhhhhhhhhhhhhhhhhh..... Ok here goes >.<\[y =2x -1\]

    • one year ago
  95. bettyboop8904
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    no but good try let's go through it step by step. I admit it's a little challenging with all the sign changes

    • one year ago
  96. bettyboop8904
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    what did you get for the slope?

    • one year ago
  97. MasuKasu
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    Where's my Fail Whale when I need it? xD

    • one year ago
  98. bettyboop8904
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    = )

    • one year ago
  99. MasuKasu
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    m=2

    • one year ago
  100. bettyboop8904
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    ok that's probably where it went wrong

    • one year ago
  101. bettyboop8904
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    so how did you set it up? which set of points did you put first?

    • one year ago
  102. MasuKasu
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    We have to be fast though. I have to leave for work in 15 minutes o.o

    • one year ago
  103. bettyboop8904
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    I'll be sure of it = )

    • one year ago
  104. MasuKasu
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    This is hard. One sec.

    • one year ago
  105. MasuKasu
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    |dw:1359326845829:dw|

    • one year ago
  106. MasuKasu
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    |dw:1359326969637:dw|

    • one year ago
  107. bettyboop8904
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    I see what you did you put the values in the wrong locations

    • one year ago
  108. MasuKasu
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    Ahhhhhhhhhhhhhhhh! I feel dumb haha! Help me with that please?

    • one year ago
  109. bettyboop8904
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    ok you have the points: (-1,6) and (3,-2) |dw:1359327131329:dw|

    • one year ago
  110. bettyboop8904
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    that's supposed to be a 2 at the end of that second y (subscript)

    • one year ago
  111. MasuKasu
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    Oops.... Blonde moment? Or just blind? xD

    • one year ago
  112. bettyboop8904
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    |dw:1359327213071:dw|

    • one year ago
  113. bettyboop8904
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    y1 and x1 are the same set is what that says lol like I said we all have 'em lol

    • one year ago
  114. bettyboop8904
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    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

    • one year ago
  115. bettyboop8904
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    just as I did here |dw:1359327396584:dw|

    • one year ago
  116. MasuKasu
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    I did that too lol

    • one year ago
  117. bettyboop8904
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    Did you re-work it out?

    • one year ago
  118. bettyboop8904
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    If you have to leave for work I'll post how to do the full equation and the answer at the end = )

    • one year ago
  119. MasuKasu
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    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

    • one year ago
  120. bettyboop8904
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    lol kk = )

    • one year ago
  121. MasuKasu
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    m=-2

    • one year ago
  122. MasuKasu
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    Ya? lol

    • one year ago
  123. bettyboop8904
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    yes! = D

    • one year ago
  124. MasuKasu
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    YES! Ok, let me solve the rest ;D

    • one year ago
  125. bettyboop8904
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    lol kk

    • one year ago
  126. MasuKasu
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    Or try haha! I hope this is right.

    • one year ago
  127. bettyboop8904
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    I'm sure you got it = )

    • one year ago
  128. MasuKasu
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    I uh.... I'm doubtful, but here goes o.o y=-2x-5 -_-

    • one year ago
  129. bettyboop8904
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    very extremely close which points did you plug in?

    • one year ago
  130. MasuKasu
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    OH! When I brought over the -6, I left it as -6 and didn't switch it to 6

    • one year ago
  131. MasuKasu
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    y=2x+7 ??????????????????

    • one year ago
  132. bettyboop8904
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    take a deep breath you're using (-1,6) right?

    • one year ago
  133. bettyboop8904
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    = )

    • one year ago
  134. MasuKasu
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    Yeah I am lol

    • one year ago
  135. bettyboop8904
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    |dw:1359328160642:dw|

    • one year ago
  136. bettyboop8904
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    \[-2x+4=y\]

    • one year ago
  137. bettyboop8904
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    Have a good day at work = )

    • one year ago
  138. MasuKasu
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    SORRY! My laptop actually overheated. I was also kind of late to work ^^;

    • one year ago
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