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

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

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

3. MasuKasu

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

4. bettyboop8904

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

5. bettyboop8904

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

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

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

8. bettyboop8904

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

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

10. MasuKasu

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

11. bettyboop8904

yes you are correct = )

12. MasuKasu

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

13. bettyboop8904

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

14. bettyboop8904

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

15. MasuKasu

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

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

17. MasuKasu

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

18. bettyboop8904

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

20. MasuKasu

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

21. bettyboop8904

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

22. MasuKasu

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

23. MasuKasu

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

24. bettyboop8904

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

25. MasuKasu

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

26. MasuKasu

And b is the 'base', right?

27. bettyboop8904

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

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

29. bettyboop8904

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

@masukasu

31. MasuKasu

Sorry. Someone had to use my laptop.

32. bettyboop8904

that's ok = )

33. MasuKasu

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

34. MasuKasu

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

35. bettyboop8904

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

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

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

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

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

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

41. bettyboop8904

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

OH! I remember now!

43. MasuKasu

Well... that part at least

44. bettyboop8904

|dw:1359321905435:dw|

45. MasuKasu

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

46. MasuKasu

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

47. MasuKasu

lol Yeah, I loved the Illustration haha!

48. bettyboop8904

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

49. MasuKasu

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50. MasuKasu

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

51. MasuKasu

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

52. bettyboop8904

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

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

I'm a brunette lmfao

55. MasuKasu

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

56. MasuKasu

lawl xD

57. bettyboop8904

|dw:1359322879897:dw|

58. bettyboop8904

this is the way you're used to right?

59. MasuKasu

Yeah

60. bettyboop8904

ok here we go lol

61. bettyboop8904

|dw:1359322994943:dw|

62. bettyboop8904

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63. MasuKasu

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

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

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

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

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

68. bettyboop8904

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

69. bettyboop8904

yes correct! = D

70. MasuKasu

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

71. MasuKasu

Correction: $y =2x +1$ Sorry

72. bettyboop8904

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

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

74. MasuKasu

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

75. bettyboop8904

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

76. MasuKasu

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

77. MasuKasu

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

78. MasuKasu

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

79. bettyboop8904

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

80. MasuKasu

Ok (: Be back soon!

81. bettyboop8904

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

82. MasuKasu

Back! I'll figure that out real quick.

83. bettyboop8904

kk = )

84. MasuKasu

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

85. MasuKasu

Correction: y=mx+b

86. bettyboop8904

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

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

88. MasuKasu

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

89. bettyboop8904

you have to remember those

90. MasuKasu

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

91. bettyboop8904

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

92. MasuKasu

Yeahhhhh lol >.<

93. bettyboop8904

just memory bc they give you the formula in class

94. MasuKasu

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

95. bettyboop8904

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

what did you get for the slope?

97. MasuKasu

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

98. bettyboop8904

= )

99. MasuKasu

m=2

100. bettyboop8904

ok that's probably where it went wrong

101. bettyboop8904

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

102. MasuKasu

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

103. bettyboop8904

I'll be sure of it = )

104. MasuKasu

This is hard. One sec.

105. MasuKasu

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106. MasuKasu

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107. bettyboop8904

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

108. MasuKasu

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

109. bettyboop8904

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

110. bettyboop8904

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

111. MasuKasu

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

112. bettyboop8904

|dw:1359327213071:dw|

113. bettyboop8904

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

114. bettyboop8904

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

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

116. MasuKasu

I did that too lol

117. bettyboop8904

Did you re-work it out?

118. bettyboop8904

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

119. MasuKasu

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

lol kk = )

121. MasuKasu

m=-2

122. MasuKasu

Ya? lol

123. bettyboop8904

yes! = D

124. MasuKasu

YES! Ok, let me solve the rest ;D

125. bettyboop8904

lol kk

126. MasuKasu

Or try haha! I hope this is right.

127. bettyboop8904

I'm sure you got it = )

128. MasuKasu

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

129. bettyboop8904

very extremely close which points did you plug in?

130. MasuKasu

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

131. MasuKasu

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

132. bettyboop8904

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

133. bettyboop8904

= )

134. MasuKasu

Yeah I am lol

135. bettyboop8904

|dw:1359328160642:dw|

136. bettyboop8904

$-2x+4=y$

137. bettyboop8904

Have a good day at work = )

138. MasuKasu

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