Question

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

Answer 1

Hi! Welcome to OpenStudy! :D

Answer 2

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

Answer 3

y=mx+b

Answer 4

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

Answer 5

.

Answer 6

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

Answer 7

point slope formula?

Answer 8

no

Answer 9

the formla used to count slope if called slope formula

Answer 10

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 :)

Answer 11

;)

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

i'm angry on you tso xD

Answer 17

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

Answer 18

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:
\(\sf\large (y_2-y_1)x + (x_2-x_1)y + (x_1y_1 - x_2y_1) = 0\)

Answer 19

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

Answer 20

ok

Answer 21

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

Answer 22

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

Answer 23

Correct! :D

Answer 24

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

Answer 25

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

Answer 26

(5-7)divided(4+4)

Answer 27

Yes, that is how we find the slope :D

Answer 28

so it = -1/4?

Answer 29

So simplifying that we get:

\(\Large\text{Slope } = \frac{ y_2 - y_1 } { x_2 - x_1 } \\\Large= \frac{ 7 - 5}{-4 - 4} \\\Large= \frac{ 2}{-8} \\ \Large= - \frac{1}{4}\)

Answer 30

Correct, that is the slope! :D

Answer 31

how do I put it in standard form?

Answer 32

Do you know the slope-point form? :)

Answer 33

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

Answer 34

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

Answer 35

Correct! :D

Answer 36

Ok, so let's choose a point.

Which point do you want to use? (4,5) or (-4,7) ?

Answer 37

(4,5)?

Answer 38

sure!

Answer 39

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

Answer 40

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

Answer 41

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

Answer 42

correct! :D

Answer 43

Now lets make that into standard form :)

Answer 44

\(\sf\Large y - 5 = -\frac{1}{4}(x-4)\)

Lets distribute the -1/4 into the parenthesis

Remember: a(b-c) = ab - ac

Answer 45

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

Answer 46

mhmm, actually no :(

Answer 47

\(\sf\Large y - 5 = -\frac{1}{4}(x-4)\)

\(\sf\Large y - 5 = (-\frac{1}{4})(x) - (-\frac{1}{4})(4)\)

\(\sf\Large y - 5 = -\frac{1}{4}x - (-1)\)

Answer 48

Do you understand? :)

Answer 49

No explain further.

Answer 50

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

Answer 51

Lets simplify this:

\(\sf\Large -\frac{1}{4} -(-1) \)

Do you know what happens when we subtract a negative number?

Answer 52

i know a negative times a negative is a positive

Answer 53

It would become addition :)

Answer 54

So now we have

\(\sf\Large y - 5 = -\frac{1}{4}x +1\)

Lets add the -1/4x on both sides :)

Answer 55

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

Answer 56

y=-1/4x+6

Answer 57

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

Answer 58

So now we have

\(\sf\Large y + \frac{1}{4}x = -\frac{1}{4}x +\frac{1}{4}x +6\)

Simplify it :)

Answer 59

1/4x+y=6

Answer 60

And that's your answer! :D

Answer 61

That is in the form

ax + by = c

Answer 62

Thank you for cooperating @kirstenc73093 :D

And Welcome to OpenStudy! :D

Answer 63

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

Answer 64

Anytime! :D

Answer 65

Just tag me if you ever need me

You can tag me like: @thesmartone

Answer 66

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Answer 67

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

Answer 68

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:

Answer 69

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

Answer 70

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

Answer 71

Anytime! :D

Answer 72

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.

Answer 73

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.