Question

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

Haaaaalp

Answer 1

HI!!

Answer 2

Hi!

Answer 3

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?

Answer 4

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

Answer 5

not quite

Answer 6

you want to subtract, not add

Answer 7

Oh, okay. Hold on Lemme try.

Answer 8

kk

Answer 9

ok so its -8/5 ??

Answer 10

hmm \(9-6=?\)

Answer 11

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

Answer 12

lets go slow

Answer 13

Yes

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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 \[-\frac{8}{3}\]

Answer 18

okay, yes.

Answer 19

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

Answer 20

okay, got it.

Answer 21

who goes to school in the middle of august?

Answer 22

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

Answer 23

Everyone where I'm from starts in August. I know some places in California start later.

so y=mx+b?

Answer 24

wait, thats not right.

Answer 25

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

Answer 26

y-y1 = m (x-x1)

Answer 27

yeah that one

Answer 28

Okay so

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

Answer 29

ooh no

Answer 30

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 )

Answer 31

you put numbers everywhere

Answer 32

oh. gosh ok.

y+4= -8/3 (x-9)

Answer 33

looks a lot better now

Answer 34

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

Answer 35

right

Answer 36

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

Answer 37

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

Answer 38

Move the 4 to the other side?

Answer 39

no not yet

Answer 40

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

Answer 41

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

Answer 42

multiply

Answer 43

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

Answer 44

then don't "move the 4" subtract 4

Answer 45

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

Answer 46

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

Answer 47

yeah

Answer 48

cancel the 3's

Answer 49

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

Answer 50

Okay, I understand.

Answer 51

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

Answer 52

y=-8/3x+20

Answer 53

yup

Answer 54

took a while but i hope it is ok

Answer 55

Is that the final answer?

Answer 56

Thanks by the way (:

Answer 57

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

Answer 58

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

Answer 59

thanks!