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MasuKasu

  • 2 years ago

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)?

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  1. bettyboop8904
    • 2 years ago
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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?

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

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

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

  5. bettyboop8904
    • 2 years ago
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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?

  6. bettyboop8904
    • 2 years ago
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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.

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

  8. bettyboop8904
    • 2 years ago
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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

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

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

  11. bettyboop8904
    • 2 years ago
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    yes you are correct = )

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

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

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

  15. MasuKasu
    • 2 years ago
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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

  16. bettyboop8904
    • 2 years ago
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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

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

  18. bettyboop8904
    • 2 years ago
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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

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

  20. MasuKasu
    • 2 years ago
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    Pff... Sorry. I mixed my numbers up >.<

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

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

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

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

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

  26. MasuKasu
    • 2 years ago
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    And b is the 'base', right?

  27. bettyboop8904
    • 2 years ago
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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?

  28. bettyboop8904
    • 2 years ago
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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

  29. bettyboop8904
    • 2 years ago
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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

  30. bettyboop8904
    • 2 years ago
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    @masukasu

  31. MasuKasu
    • 2 years ago
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    Sorry. Someone had to use my laptop.

  32. bettyboop8904
    • 2 years ago
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    that's ok = )

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

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

  35. bettyboop8904
    • 2 years ago
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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

  36. bettyboop8904
    • 2 years ago
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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.

  37. MasuKasu
    • 2 years ago
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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.

  38. bettyboop8904
    • 2 years ago
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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 = )

  39. MasuKasu
    • 2 years ago
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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

  40. MasuKasu
    • 2 years ago
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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?

  41. bettyboop8904
    • 2 years ago
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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

  42. MasuKasu
    • 2 years ago
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    OH! I remember now!

  43. MasuKasu
    • 2 years ago
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    Well... that part at least

  44. bettyboop8904
    • 2 years ago
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    |dw:1359321905435:dw|

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

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

  47. MasuKasu
    • 2 years ago
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    lol Yeah, I loved the Illustration haha!

  48. bettyboop8904
    • 2 years ago
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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

  49. MasuKasu
    • 2 years ago
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    |dw:1359322373754:dw|

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

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

  52. bettyboop8904
    • 2 years ago
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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

  53. MasuKasu
    • 2 years ago
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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

  54. bettyboop8904
    • 2 years ago
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    I'm a brunette lmfao

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

  56. MasuKasu
    • 2 years ago
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    lawl xD

  57. bettyboop8904
    • 2 years ago
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    |dw:1359322879897:dw|

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

  59. MasuKasu
    • 2 years ago
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    Yeah

  60. bettyboop8904
    • 2 years ago
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    ok here we go lol

  61. bettyboop8904
    • 2 years ago
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    |dw:1359322994943:dw|

  62. bettyboop8904
    • 2 years ago
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    |dw:1359323398039:dw|

  63. MasuKasu
    • 2 years ago
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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.

  64. bettyboop8904
    • 2 years ago
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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

  65. MasuKasu
    • 2 years ago
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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.

  66. bettyboop8904
    • 2 years ago
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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 = )

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

  68. bettyboop8904
    • 2 years ago
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    Ok so we have: |dw:1359323569725:dw||dw:1359323806202:dw|

  69. bettyboop8904
    • 2 years ago
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    yes correct! = D

  70. MasuKasu
    • 2 years ago
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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?

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

  72. bettyboop8904
    • 2 years ago
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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?

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

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

  75. bettyboop8904
    • 2 years ago
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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

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

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

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

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

  80. MasuKasu
    • 2 years ago
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    Ok (: Be back soon!

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

  82. MasuKasu
    • 2 years ago
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    Back! I'll figure that out real quick.

  83. bettyboop8904
    • 2 years ago
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    kk = )

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

  85. MasuKasu
    • 2 years ago
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    Correction: y=mx+b

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

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

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

  89. bettyboop8904
    • 2 years ago
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    you have to remember those

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

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

  92. MasuKasu
    • 2 years ago
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    Yeahhhhh lol >.<

  93. bettyboop8904
    • 2 years ago
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    just memory bc they give you the formula in class

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

  95. bettyboop8904
    • 2 years ago
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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

  96. bettyboop8904
    • 2 years ago
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    what did you get for the slope?

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

  98. bettyboop8904
    • 2 years ago
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    = )

  99. MasuKasu
    • 2 years ago
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    m=2

  100. bettyboop8904
    • 2 years ago
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    ok that's probably where it went wrong

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

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

  103. bettyboop8904
    • 2 years ago
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    I'll be sure of it = )

  104. MasuKasu
    • 2 years ago
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    This is hard. One sec.

  105. MasuKasu
    • 2 years ago
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    |dw:1359326845829:dw|

  106. MasuKasu
    • 2 years ago
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    |dw:1359326969637:dw|

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

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

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

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

  111. MasuKasu
    • 2 years ago
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    Oops.... Blonde moment? Or just blind? xD

  112. bettyboop8904
    • 2 years ago
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    |dw:1359327213071:dw|

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

  114. bettyboop8904
    • 2 years ago
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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

  115. bettyboop8904
    • 2 years ago
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    just as I did here |dw:1359327396584:dw|

  116. MasuKasu
    • 2 years ago
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    I did that too lol

  117. bettyboop8904
    • 2 years ago
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    Did you re-work it out?

  118. bettyboop8904
    • 2 years ago
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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 = )

  119. MasuKasu
    • 2 years ago
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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

  120. bettyboop8904
    • 2 years ago
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    lol kk = )

  121. MasuKasu
    • 2 years ago
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    m=-2

  122. MasuKasu
    • 2 years ago
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    Ya? lol

  123. bettyboop8904
    • 2 years ago
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    yes! = D

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

  125. bettyboop8904
    • 2 years ago
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    lol kk

  126. MasuKasu
    • 2 years ago
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    Or try haha! I hope this is right.

  127. bettyboop8904
    • 2 years ago
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    I'm sure you got it = )

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

  129. bettyboop8904
    • 2 years ago
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    very extremely close which points did you plug in?

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

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

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

  133. bettyboop8904
    • 2 years ago
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    = )

  134. MasuKasu
    • 2 years ago
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    Yeah I am lol

  135. bettyboop8904
    • 2 years ago
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    |dw:1359328160642:dw|

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

  137. bettyboop8904
    • 2 years ago
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    Have a good day at work = )

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

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