anonymous
  • anonymous
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)?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
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?
anonymous
  • anonymous
you want to obtain y=mx+b and that formula is the formula for slope (aka "m") @masukasu
anonymous
  • anonymous
How do I know what numbers to assign to y and x?

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anonymous
  • anonymous
so this is what it will look like once you plug the points in: \[\frac{ (3) - (-1) }{ (2)-(0) }\]
anonymous
  • anonymous
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?
anonymous
  • anonymous
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.
anonymous
  • anonymous
So, (0, -1) and (2, 3) would look like this with their appropriate values: (x, -y) and (x, y) right?
anonymous
  • anonymous
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
anonymous
  • anonymous
so go ahead and solve for the slope (m) and tell me what you get
anonymous
  • anonymous
But, the example of the order of my values(in my last comment) are correct, right?
anonymous
  • anonymous
yes you are correct = )
anonymous
  • anonymous
Ah! Thank you. I'll try to solve the problem. One minute (:
anonymous
  • anonymous
now that is only part of it, there is another equation to arrive to the final equation
anonymous
  • anonymous
once you find the slope I can tell you the next part = )
anonymous
  • anonymous
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
anonymous
  • anonymous
Oh I'm sorry, the subscript 1 and 2 are only there to decipher between the different values those aren't exponents
anonymous
  • anonymous
Ohhh ok, thank you. I couldn't remember the right terminology either, sorry. But, I think it's: \[\frac{ 4 }{ -1 }\]
anonymous
  • anonymous
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
anonymous
  • anonymous
your numerator is correct double check your denominator (2-0) = ?
anonymous
  • anonymous
Pff... Sorry. I mixed my numbers up >.<
anonymous
  • anonymous
no apologies = ) I was just on here earlier getting help and I did the same thing lol ; D
anonymous
  • anonymous
Essentially it comes out to \[\frac{ 2 }{ 1 }\]
anonymous
  • anonymous
lol I guess we all make mistakes haha! It's how we learn.
anonymous
  • anonymous
correct = ) so that is your "m" or slope
anonymous
  • anonymous
yay! Alright, so that should be written out like so: \[y =2x +b\]
anonymous
  • anonymous
And b is the 'base', right?
anonymous
  • anonymous
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?
anonymous
  • anonymous
I can't remember if it is called the base but that will be your y-intercept once you graph it
anonymous
  • anonymous
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
anonymous
  • anonymous
@masukasu
anonymous
  • anonymous
Sorry. Someone had to use my laptop.
anonymous
  • anonymous
that's ok = )
anonymous
  • anonymous
Ok, I'm going to solve that. One minute (:
anonymous
  • anonymous
Wait... Do I NEED the parenthesis around the numbers? Or does it not really change anything?
anonymous
  • anonymous
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
anonymous
  • anonymous
but it will only screw things up when you have to solve for y if you forget to change the sign of the -1.
anonymous
  • anonymous
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.
anonymous
  • anonymous
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 = )
anonymous
  • anonymous
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
anonymous
  • anonymous
Factoring... Uh lol Is that factoring? I can't remember. Am I able to reverse the equation like I did though?
anonymous
  • anonymous
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
anonymous
  • anonymous
OH! I remember now!
anonymous
  • anonymous
Well... that part at least
anonymous
  • anonymous
|dw:1359321905435:dw|
anonymous
  • anonymous
And then that would turn into \[y =2x-12\] right?
anonymous
  • anonymous
No wait.... Ugh! I think that's wrong actually.
anonymous
  • anonymous
lol Yeah, I loved the Illustration haha!
anonymous
  • anonymous
no look at it this way: \[y= 2x+(-4) +3\] \[y=2x +(-1) \] \[y=2x-1\] Does that make sense? = D
anonymous
  • anonymous
|dw:1359322373754:dw|
anonymous
  • anonymous
Trying to rework the problem so I can better understand it...
anonymous
  • anonymous
(2 x X)=2x (2 x 2)=4 y=2x ???????????? I can't figure out how you got the -4
anonymous
  • anonymous
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
anonymous
  • anonymous
I uh.... Well, I have blonde moments too lol And I've black hair and I'm Asian haha! So, no worries :P
anonymous
  • anonymous
I'm a brunette lmfao
anonymous
  • anonymous
It's the 2x+(-4) part that gets me
anonymous
  • anonymous
lawl xD
anonymous
  • anonymous
|dw:1359322879897:dw|
anonymous
  • anonymous
this is the way you're used to right?
anonymous
  • anonymous
Yeah
anonymous
  • anonymous
ok here we go lol
anonymous
  • anonymous
|dw:1359322994943:dw|
anonymous
  • anonymous
|dw:1359323398039:dw|
anonymous
  • anonymous
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.
anonymous
  • anonymous
it's always good to make an equation have positives so y-(+3) can also be written as y+(-3) its the same thing
anonymous
  • anonymous
Trying to understand this... I always had a hard time understanding these problems because of all the positives switching to negatives and vice versa.
anonymous
  • anonymous
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 = )
anonymous
  • anonymous
Ohhh so that's what you did +(-4), right?
anonymous
  • anonymous
Ok so we have: |dw:1359323569725:dw||dw:1359323806202:dw|
anonymous
  • anonymous
yes correct! = D
anonymous
  • anonymous
\[y=2x + \left( -4+3 \right)\] right? Which becomes \[y =2x\] With the +(-4), that + sign pretty much comes out of nowhere, right?
anonymous
  • anonymous
Correction: \[y =2x +1\] Sorry
anonymous
  • anonymous
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?
anonymous
  • anonymous
Do you feel confident that you can do another one by yourself?
anonymous
  • anonymous
I would like to try (: So, shoot! Let's see if I can do this.
anonymous
  • anonymous
ok let me just quickly work one out to make sure its not messy lol like no fractions i hate fractions lol
anonymous
  • anonymous
And I had to repeat Pre-Algebra once, went on to Algebra 1, and didn't do too well there.
anonymous
  • anonymous
Ok! And you're 50,000,000 times smarter than me haha!
anonymous
  • anonymous
While you're doing that, I'm going to take a super fast shower. Like... 5-10 minutes.
anonymous
  • anonymous
ok when you get back I will have the equation already up = )
anonymous
  • anonymous
Ok (: Be back soon!
anonymous
  • anonymous
What is the equation of a line that passes through points (-1,6) and (3,-2)?
anonymous
  • anonymous
Back! I'll figure that out real quick.
anonymous
  • anonymous
kk = )
anonymous
  • anonymous
So, I want to figure out y+mx+b right?
anonymous
  • anonymous
Correction: y=mx+b
anonymous
  • anonymous
correct and you will use two formulas to figure that out: \[\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\] \[m(x-x _{1})=y-y _{1}\]
anonymous
  • anonymous
correction: \[m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]
anonymous
  • anonymous
Ok, so does that second formula come from somewhere or do you have to remember it? lol
anonymous
  • anonymous
you have to remember those
anonymous
  • anonymous
Sorry. Does it come from somewhere within the first formula, or does it come from nowhere, except memory?
anonymous
  • anonymous
it sucks bc there is so much memorization in math = (
anonymous
  • anonymous
Yeahhhhh lol >.<
anonymous
  • anonymous
just memory bc they give you the formula in class
anonymous
  • anonymous
Uhhhhhhhhhhhhhhhhhhhhhhhhhh..... Ok here goes >.<\[y =2x -1\]
anonymous
  • anonymous
no but good try let's go through it step by step. I admit it's a little challenging with all the sign changes
anonymous
  • anonymous
what did you get for the slope?
anonymous
  • anonymous
Where's my Fail Whale when I need it? xD
anonymous
  • anonymous
= )
anonymous
  • anonymous
m=2
anonymous
  • anonymous
ok that's probably where it went wrong
anonymous
  • anonymous
so how did you set it up? which set of points did you put first?
anonymous
  • anonymous
We have to be fast though. I have to leave for work in 15 minutes o.o
anonymous
  • anonymous
I'll be sure of it = )
anonymous
  • anonymous
This is hard. One sec.
anonymous
  • anonymous
|dw:1359326845829:dw|
anonymous
  • anonymous
|dw:1359326969637:dw|
anonymous
  • anonymous
I see what you did you put the values in the wrong locations
anonymous
  • anonymous
Ahhhhhhhhhhhhhhhh! I feel dumb haha! Help me with that please?
anonymous
  • anonymous
ok you have the points: (-1,6) and (3,-2) |dw:1359327131329:dw|
anonymous
  • anonymous
that's supposed to be a 2 at the end of that second y (subscript)
anonymous
  • anonymous
Oops.... Blonde moment? Or just blind? xD
anonymous
  • anonymous
|dw:1359327213071:dw|
anonymous
  • anonymous
y1 and x1 are the same set is what that says lol like I said we all have 'em lol
anonymous
  • anonymous
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
anonymous
  • anonymous
just as I did here |dw:1359327396584:dw|
anonymous
  • anonymous
I did that too lol
anonymous
  • anonymous
Did you re-work it out?
anonymous
  • anonymous
If you have to leave for work I'll post how to do the full equation and the answer at the end = )
anonymous
  • anonymous
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
anonymous
  • anonymous
lol kk = )
anonymous
  • anonymous
m=-2
anonymous
  • anonymous
Ya? lol
anonymous
  • anonymous
yes! = D
anonymous
  • anonymous
YES! Ok, let me solve the rest ;D
anonymous
  • anonymous
lol kk
anonymous
  • anonymous
Or try haha! I hope this is right.
anonymous
  • anonymous
I'm sure you got it = )
anonymous
  • anonymous
I uh.... I'm doubtful, but here goes o.o y=-2x-5 -_-
anonymous
  • anonymous
very extremely close which points did you plug in?
anonymous
  • anonymous
OH! When I brought over the -6, I left it as -6 and didn't switch it to 6
anonymous
  • anonymous
y=2x+7 ??????????????????
anonymous
  • anonymous
take a deep breath you're using (-1,6) right?
anonymous
  • anonymous
= )
anonymous
  • anonymous
Yeah I am lol
anonymous
  • anonymous
|dw:1359328160642:dw|
anonymous
  • anonymous
\[-2x+4=y\]
anonymous
  • anonymous
Have a good day at work = )
anonymous
  • anonymous
SORRY! My laptop actually overheated. I was also kind of late to work ^^;

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