anonymous
  • anonymous
Write an equation in standard form of the line passing through the points (4,5) and (-4,7) I know standard for is ax+by=c, but I am not sure how to solve this or set it up
Linear Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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TheSmartOne
  • TheSmartOne
Hi! Welcome to OpenStudy! :D
TheSmartOne
  • TheSmartOne
First of all, do you know the slope formula? @KristenSkate
anonymous
  • anonymous
y=mx+b

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More answers

TheSmartOne
  • TheSmartOne
That's the slope-intercept form. But do you know the slope formula?
dan815
  • dan815
.
AlexandervonHumboldt2
  • AlexandervonHumboldt2
the slope formula is \[\frac{ y_1-y_2 }{ x_1-x_2 }\] where (x1, y1) and (x2, y2) are your points.
anonymous
  • anonymous
point slope formula?
AlexandervonHumboldt2
  • AlexandervonHumboldt2
no
AlexandervonHumboldt2
  • AlexandervonHumboldt2
the formla used to count slope if called slope formula
TheSmartOne
  • TheSmartOne
No, I was talking about the slope formula. The formula that you use to find the slope when you are given two points of a line. :) Alexander has provided us with the formula :)
AlexandervonHumboldt2
  • AlexandervonHumboldt2
;)
AlexandervonHumboldt2
  • AlexandervonHumboldt2
so first lets write the equation in slope-intercept form, and then convert it into standard.
TheSmartOne
  • TheSmartOne
Well, anyways, I found a way to get the answer to your question without having to find the slope formula! :D
AlexandervonHumboldt2
  • AlexandervonHumboldt2
so we have the slope: (5-7)/(4+4)=-2/8=-1/4
TheSmartOne
  • TheSmartOne
@AlexandervonHumboldt2 Let's guide the user, please :)
AlexandervonHumboldt2
  • AlexandervonHumboldt2
i'm angry on you tso xD
anonymous
  • anonymous
okay so I subtract 7-5 on the numerator and then for the denominator I do -4-4?
TheSmartOne
  • TheSmartOne
So if you want to find the linear equation of a line that passes through points \(\sf\Large (x_1,y_1), ~and~(x_2,y_2)\) in the form: \(\sf\Large Ax+By+c = 0\) then you use the formula: \(\sf\large (y_2-y_1)x + (x_2-x_1)y + (x_1y_1 - x_2y_1) = 0\)
TheSmartOne
  • TheSmartOne
Sure, it might seem a little complex at first. But let's break it down, ok? :)
anonymous
  • anonymous
ok
TheSmartOne
  • TheSmartOne
We are given the points (4,5) and (-4,7), right? :)
anonymous
  • anonymous
yes so 4 is X1 and -4 is X2 5 is Y1 and 7 is Y2
TheSmartOne
  • TheSmartOne
Correct! :D
TheSmartOne
  • TheSmartOne
So, now we just plug that into the formula :)
TheSmartOne
  • TheSmartOne
Once we do it this way, if you want, we can do it another way too! So that way you don't need to solve it one way! :D
anonymous
  • anonymous
(5-7)divided(4+4)
TheSmartOne
  • TheSmartOne
Yes, that is how we find the slope :D
anonymous
  • anonymous
so it = -1/4?
TheSmartOne
  • TheSmartOne
So simplifying that we get: \(\Large\text{Slope } = \frac{ y_2 - y_1 } { x_2 - x_1 } \\\Large= \frac{ 7 - 5}{-4 - 4} \\\Large= \frac{ 2}{-8} \\ \Large= - \frac{1}{4}\)
TheSmartOne
  • TheSmartOne
Correct, that is the slope! :D
anonymous
  • anonymous
how do I put it in standard form?
TheSmartOne
  • TheSmartOne
Do you know the slope-point form? :)
TheSmartOne
  • TheSmartOne
first we can easily make it in slope-point form, and then convert it to standard form :D
anonymous
  • anonymous
y-y1=m(x-x1) is that it?
TheSmartOne
  • TheSmartOne
Correct! :D
TheSmartOne
  • TheSmartOne
Ok, so let's choose a point. Which point do you want to use? (4,5) or (-4,7) ?
anonymous
  • anonymous
(4,5)?
TheSmartOne
  • TheSmartOne
sure!
TheSmartOne
  • TheSmartOne
ok so we need to plug in the point (4,5) and the slope which is -1/4 into it 4 is x1, and 5 is y1 m is the slope which is -1/4
TheSmartOne
  • TheSmartOne
So what do we get when we plug that into y-y1=m(x-x1)
anonymous
  • anonymous
y-5=-1/4(x-4) is that it?
TheSmartOne
  • TheSmartOne
correct! :D
TheSmartOne
  • TheSmartOne
Now lets make that into standard form :)
TheSmartOne
  • TheSmartOne
\(\sf\Large y - 5 = -\frac{1}{4}(x-4)\) Lets distribute the -1/4 into the parenthesis Remember: a(b-c) = ab - ac
anonymous
  • anonymous
when distributing -1/4(-4) would it cancel out 4 of the denominator making it 1?
TheSmartOne
  • TheSmartOne
mhmm, actually no :(
TheSmartOne
  • TheSmartOne
\(\sf\Large y - 5 = -\frac{1}{4}(x-4)\) \(\sf\Large y - 5 = (-\frac{1}{4})(x) - (-\frac{1}{4})(4)\) \(\sf\Large y - 5 = -\frac{1}{4}x - (-1)\)
TheSmartOne
  • TheSmartOne
Do you understand? :)
pooja195
  • pooja195
No explain further.
TheSmartOne
  • TheSmartOne
@KristenSkate So, now we need to simplify it further. :)
TheSmartOne
  • TheSmartOne
Lets simplify this: \(\sf\Large -\frac{1}{4} -(-1) \) Do you know what happens when we subtract a negative number?
anonymous
  • anonymous
i know a negative times a negative is a positive
TheSmartOne
  • TheSmartOne
It would become addition :)
TheSmartOne
  • TheSmartOne
So now we have \(\sf\Large y - 5 = -\frac{1}{4}x +1\) Lets add the -1/4x on both sides :)
TheSmartOne
  • TheSmartOne
And finally, we have to add 5 on both sides :D
anonymous
  • anonymous
y=-1/4x+6
TheSmartOne
  • TheSmartOne
And now all we need to do is add 1/4x on both sides :D
TheSmartOne
  • TheSmartOne
So now we have \(\sf\Large y + \frac{1}{4}x = -\frac{1}{4}x +\frac{1}{4}x +6\) Simplify it :)
anonymous
  • anonymous
1/4x+y=6
TheSmartOne
  • TheSmartOne
And that's your answer! :D
TheSmartOne
  • TheSmartOne
That is in the form ax + by = c
TheSmartOne
  • TheSmartOne
Thank you for cooperating @kirstenc73093 :D And Welcome to OpenStudy! :D
anonymous
  • anonymous
thanks so much I hope I can have you help me again!!
TheSmartOne
  • TheSmartOne
Anytime! :D
TheSmartOne
  • TheSmartOne
Just tag me if you ever need me You can tag me like: @thesmartone
TheSmartOne
  • TheSmartOne
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anonymous
  • anonymous
oh okay. how can I give you a good rating?
TheSmartOne
  • TheSmartOne
Ah, I'm not a Qualified Helper, but I'm just as great as one. So the QH's backed off when they saw me helping. But they're just as great. :P You can rate them by clicking this button: |dw:1447460546674:dw|
TheSmartOne
  • TheSmartOne
That button can be found at the top of your screen :)
TheSmartOne
  • TheSmartOne
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anonymous
  • anonymous
@TheSmartOne you should be a paid tutor! You awesome thanks for being patient with me
TheSmartOne
  • TheSmartOne
Anytime! :D
JMark
  • JMark
using slope point form, slope m = 7 - 5/-4-4 = 2/-8 = -1/4 equation, (y - 5) = -1/4(x - 4) or 4(y-5)+x-4 = 4y +x=24.
TheSmartOne
  • TheSmartOne
You're late @jmark 23 days late. And the asker already got the answer too. So, I see no reason for you to have replied to this post.

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