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)?

- anonymous

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- 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

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

- anonymous

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

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## More answers

- anonymous

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

- 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

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

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

- 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

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

- anonymous

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

- anonymous

yes you are correct = )

- anonymous

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

- anonymous

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

- anonymous

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

- 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

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

- anonymous

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

- 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

your numerator is correct double check your denominator (2-0) = ?

- anonymous

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

- anonymous

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

- anonymous

Essentially it comes out to \[\frac{ 2 }{ 1 }\]

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

And b is the 'base', right?

- 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

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

- 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

@masukasu

- anonymous

Sorry. Someone had to use my laptop.

- anonymous

that's ok = )

- anonymous

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

- anonymous

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

- 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

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

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

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

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

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

- 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

OH! I remember now!

- anonymous

Well... that part at least

- anonymous

|dw:1359321905435:dw|

- anonymous

And then that would turn into \[y =2x-12\] right?

- anonymous

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

- anonymous

lol Yeah, I loved the Illustration haha!

- anonymous

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

- anonymous

|dw:1359322373754:dw|

- anonymous

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

- anonymous

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

- 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

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

- anonymous

I'm a brunette lmfao

- anonymous

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

- anonymous

lawl xD

- anonymous

|dw:1359322879897:dw|

- anonymous

this is the way you're used to right?

- anonymous

Yeah

- anonymous

ok here we go lol

- anonymous

|dw:1359322994943:dw|

- anonymous

|dw:1359323398039:dw|

- 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

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

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

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

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

- anonymous

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

- anonymous

yes correct! = D

- 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

Correction: \[y =2x +1\]
Sorry

- 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

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

Ok (: Be back soon!

- anonymous

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

- anonymous

Back! I'll figure that out real quick.

- anonymous

kk = )

- anonymous

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

- anonymous

Correction: y=mx+b

- 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

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

- anonymous

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

- anonymous

you have to remember those

- anonymous

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

- anonymous

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

- anonymous

Yeahhhhh lol >.<

- anonymous

just memory bc they give you the formula in class

- anonymous

Uhhhhhhhhhhhhhhhhhhhhhhhhhh..... Ok here goes >.<\[y =2x -1\]

- 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

what did you get for the slope?

- anonymous

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

- anonymous

= )

- anonymous

m=2

- anonymous

ok that's probably where it went wrong

- anonymous

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

- anonymous

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

- anonymous

I'll be sure of it = )

- anonymous

This is hard. One sec.

- anonymous

|dw:1359326845829:dw|

- anonymous

|dw:1359326969637:dw|

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

|dw:1359327213071:dw|

- anonymous

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

- 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

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

- anonymous

I did that too lol

- anonymous

Did you re-work it out?

- anonymous

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

- 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

lol kk = )

- anonymous

m=-2

- anonymous

Ya? lol

- anonymous

yes! = D

- anonymous

YES! Ok, let me solve the rest ;D

- anonymous

lol kk

- anonymous

Or try haha! I hope this is right.

- anonymous

I'm sure you got it = )

- anonymous

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

- anonymous

very extremely close which points did you plug in?

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

= )

- anonymous

Yeah I am lol

- anonymous

|dw:1359328160642:dw|

- anonymous

\[-2x+4=y\]

- anonymous

Have a good day at work = )

- anonymous

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

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