Determine the standard form of the equation of the line that passes through (9, -4) and (6, 4)
Haaaaalp

- anonymous

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- misty1212

HI!!

- anonymous

Hi!

- misty1212

first we need the slope, because no matter what, if you want the equation of a line you need to have the slope
do you know how to find ti?

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## More answers

- anonymous

that would be -4+4 over 9+4 right?

- misty1212

not quite

- misty1212

you want to subtract, not add

- anonymous

Oh, okay. Hold on Lemme try.

- misty1212

kk

- anonymous

ok so its -8/5 ??

- misty1212

hmm \(9-6=?\)

- anonymous

oh dang! I was doing -4. My bad. So it's 4.

- misty1212

lets go slow

- anonymous

Yes

- misty1212

(9, -4) and (6, 4)

- misty1212

first we do it the think way, then we do it the math teacher way

- anonymous

Okay, it's like the third day of school. My brain doesn't work yet! sorry ahah.

- misty1212

from 6 to 9 in the x is right 3 units
from 4 to -4 in the y is down 8 units
right 3, down 8
slope is \[-\frac{8}{3}\]

- anonymous

okay, yes.

- misty1212

now the math teacher way
\[\frac{y_2-y_1}{x_2-*x_1}=\frac{-4-4}{9-6}=-\frac{8}{3}\] or
\[\frac{4-(-4)}{6-9}=\frac{8}{-3}=-\frac{8}{3}\] either way

- anonymous

okay, got it.

- misty1212

who goes to school in the middle of august?

- misty1212

ok no matter, now we have the the slope, and we can use the"point slope" formula because we have two points to choose form

- anonymous

Everyone where I'm from starts in August. I know some places in California start later.
so y=mx+b?

- anonymous

wait, thats not right.

- misty1212

no that is the "slope intercept " form we are not there yet

- anonymous

y-y1 = m (x-x1)

- misty1212

yeah that one

- anonymous

Okay so
-4 - 4 = -8/3 (9 - 6) ?

- misty1212

ooh no

- misty1212

the x and y in the formula are the variables you see in the answer
only the \(x_1\) and \(y_1\) are numbers (as well as m )

- misty1212

you put numbers everywhere

- anonymous

oh. gosh ok.
y+4= -8/3 (x-9)

- misty1212

looks a lot better now

- anonymous

subtracting a negative turns it into an addition basically, right?

- misty1212

right

- misty1212

now you should probably put it in "slope intercept" form aka solve for y

- misty1212

you know how to do that? takes the same two steps every time

- anonymous

Move the 4 to the other side?

- misty1212

no not yet

- misty1212

first distribute the \(-\frac{8}{3}\) on the left

- anonymous

oh yeah. so I multiply it or add it to the left?

- misty1212

multiply

- misty1212

\[y+4=-\frac{8}{3}+24\] if my arithmetic is correct

- misty1212

then don't "move the 4" subtract 4

- misty1212

sorry, typo there i meant \[y+4=-\frac{8}{3}x+24\]
i dropped the x by mistake

- anonymous

wait, where did 24 come? distributing the slope on the right side?

- misty1212

yeah

- misty1212

cancel the 3's

- misty1212

\[-\frac{8}{3}\times (-9)=3\times 8=24\]

- anonymous

Okay, I understand.

- misty1212

so now we are at
\[y+4=-\frac{8}{3}x+24\] subtract 4 from both sides and you are done

- anonymous

y=-8/3x+20

- misty1212

yup

- misty1212

took a while but i hope it is ok

- anonymous

Is that the final answer?

- anonymous

Thanks by the way (:

- misty1212

yeah it is the "final answer" as they say on tv you are quite welcome \[\color\magenta\heartsuit\]

- anonymous

haha, of course! I'll give you a medal.

- misty1212

thanks!

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