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

- anonymous

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- schrodinger

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- TheSmartOne

Hi! Welcome to OpenStudy! :D

- TheSmartOne

First of all, do you know the slope formula? @KristenSkate

- anonymous

y=mx+b

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## More answers

- TheSmartOne

That's the slope-intercept form. But do you know the slope formula?

- dan815

.

- AlexandervonHumboldt2

the slope formula is \[\frac{ y_1-y_2 }{ x_1-x_2 }\] where (x1, y1) and (x2, y2) are your points.

- anonymous

point slope formula?

- AlexandervonHumboldt2

no

- AlexandervonHumboldt2

the formla used to count slope if called slope formula

- 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

so first lets write the equation in slope-intercept form, and then convert it into standard.

- TheSmartOne

Well, anyways, I found a way to get the answer to your question without having to find the slope formula! :D

- AlexandervonHumboldt2

so we have the slope: (5-7)/(4+4)=-2/8=-1/4

- TheSmartOne

@AlexandervonHumboldt2 Let's guide the user, please :)

- AlexandervonHumboldt2

i'm angry on you tso xD

- anonymous

okay so I subtract 7-5 on the numerator and then for the denominator I do -4-4?

- 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

Sure, it might seem a little complex at first. But let's break it down, ok? :)

- anonymous

ok

- TheSmartOne

We are given the points (4,5) and (-4,7), right? :)

- anonymous

yes so 4 is X1 and -4 is X2
5 is Y1 and 7 is Y2

- TheSmartOne

Correct! :D

- TheSmartOne

So, now we just plug that into the formula :)

- 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

(5-7)divided(4+4)

- TheSmartOne

Yes, that is how we find the slope :D

- anonymous

so it = -1/4?

- 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

Correct, that is the slope! :D

- anonymous

how do I put it in standard form?

- TheSmartOne

Do you know the slope-point form? :)

- TheSmartOne

first we can easily make it in slope-point form, and then convert it to standard form :D

- anonymous

y-y1=m(x-x1)
is that it?

- TheSmartOne

Correct! :D

- TheSmartOne

Ok, so let's choose a point.
Which point do you want to use? (4,5) or (-4,7) ?

- anonymous

(4,5)?

- TheSmartOne

sure!

- 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

So what do we get when we plug that into
y-y1=m(x-x1)

- anonymous

y-5=-1/4(x-4)
is that it?

- TheSmartOne

correct! :D

- TheSmartOne

Now lets make that into standard form :)

- 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

when distributing -1/4(-4) would it cancel out 4 of the denominator making it 1?

- TheSmartOne

mhmm, actually no :(

- 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

Do you understand? :)

- pooja195

No explain further.

- TheSmartOne

@KristenSkate So, now we need to simplify it further. :)

- TheSmartOne

Lets simplify this:
\(\sf\Large -\frac{1}{4} -(-1) \)
Do you know what happens when we subtract a negative number?

- anonymous

i know a negative times a negative is a positive

- TheSmartOne

It would become addition :)

- TheSmartOne

So now we have
\(\sf\Large y - 5 = -\frac{1}{4}x +1\)
Lets add the -1/4x on both sides :)

- TheSmartOne

And finally, we have to add 5 on both sides :D

- anonymous

y=-1/4x+6

- TheSmartOne

And now all we need to do is add 1/4x on both sides :D

- TheSmartOne

So now we have
\(\sf\Large y + \frac{1}{4}x = -\frac{1}{4}x +\frac{1}{4}x +6\)
Simplify it :)

- anonymous

1/4x+y=6

- TheSmartOne

And that's your answer! :D

- TheSmartOne

That is in the form
ax + by = c

- TheSmartOne

Thank you for cooperating @kirstenc73093 :D
And Welcome to OpenStudy! :D

- anonymous

thanks so much I hope I can have you help me again!!

- TheSmartOne

Anytime! :D

- TheSmartOne

Just tag me if you ever need me
You can tag me like: @thesmartone

- TheSmartOne

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- anonymous

oh okay. how can I give you a good rating?

- 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:
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- TheSmartOne

That button can be found at the top of your screen :)

- TheSmartOne

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- anonymous

@TheSmartOne you should be a paid tutor! You awesome thanks for being patient with me

- TheSmartOne

Anytime! :D

- 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

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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