Question

write the equation of the line in slope-inercept form that passes through the points (-2,6) and (-1,4)
PLEASEE HELP, Will give medal.

Answer 1

First you need to find the slope, do you know how to?

Answer 2

no

Answer 3

use formula:

y2 - y1
-------
x2 - x1

you have points (-2,6) -> (x1,y1)
and (-1,4) -> (x2,y2)

Answer 4

ok hold on

Answer 5

wait im confused is it suppose to be written -1-6 for the first one?

Answer 6

for the top

Answer 7

is it -1-6/4--2 ?

Answer 8

is the slope -7/6 ?

Answer 9

i tend to misplace the values ... so i do a different setup and move the points so that one of the is at the origin; then i can read the slope as y/x off the other point

(-2,6) and (-1,4)
+2-6 +2-6
---------------
0 0 1 -2 , its not going to be -7/6

Answer 10

OK, im sorry but that just confused me more,

Answer 11

how so?

Answer 12

the way you set it up, looks as if i have to add everything

Answer 13

there is addition involved; but the setup is just organizing it all

Answer 14

im subtracting the parts of one point, from the parts of the other is all

Answer 15

i know that in order to zero out (-2,6), i have to add 2 and subtract 6:

(-2+2,6-6) = (0,0) ; what you do to one point, do to the other

(-1+2,4-6) = (1,-2) .... now slope is defined as y/x

Answer 16

oooh, ok i get you, no one ever taught me that way

Answer 17

yeah, its just the mechanics behind the formula :)

Answer 18

ok, lets not talk in mathematical terms, because then your going to loose me again LOL

Answer 19

fine :) can you define the slope using the point (1,-2) now?

Answer 20

nope, but i understood what you did before.

Answer 21

when given a point (x,y), we cen define the slope from the origin as: y/x

Answer 22

so am i suppose to -1 and add 2

Answer 23

(1,-2) has the slope: -2/1, or simply, -2

Answer 24

oh ok, so you just switched x,y to y,x

Answer 25

?

Answer 26

visually, yes ... and divided them

Answer 27

ok

Answer 28

so you agree that the slope of (1,-2) from the origin is: -2/1, or just -2 right?

Answer 29

yes

Answer 30

now we just have to form the proper equation that they are asking for ... slope intercept

Answer 31

yea, you need to like break that down in nano details because i dont know how to do that either

Answer 32

with the information we have, we can form the "\(point\)-\(slope\)" form and work it into the "\(slope\)-\(intercept\)"

Answer 33

umm mhm

Answer 34

which one of the given points is your favorite? since it doesnt matter which one we need to use ....

Answer 35

im guessing Point slope, i dont know what either of them do by the way

Answer 36

we are given the points (-2,6) and (-1,4); we can use either point, and the slope that we found, to form what is called the: "\(point-slope\)" notice that this from uses a POINT and the SLOPE, hence the name ....

Answer 37

so we subtracting the point and slope? The slope we just got and the pint i still dont no

Answer 38

Point*

Answer 39

thats a hypen (-) , not a subtraction .... its just the name of the format that we can build with the information we have:

the format uses as point (a,b), and a slope (m) to build the equation:
\(y=m(x-a)+b\)

Answer 40

oh ok

Answer 41

lets use one of the points given: (-2,6); and the slope that we found (-2) and build this format:
\[y=m(x-a)+b~~\to\to\to~~y=-2(x-(-2))+6\]
or simply\[y=-2(x+2)+6\]
we are almost done ...

Answer 42

so all i know right now is M is supposed to be changed to -2

Answer 43

ok i got you

Answer 44

good, m changes to -2, and (a,b) is either point ... i just used the closest one :)

now we want to work this int the \(slope-intercept\) form which has the format:
\(y=mx+c\)

Answer 45

isnt it supposed to be b instead of c?

Answer 46

y=mx+b ??

Answer 47

since i already used "b" while naming the point, i really didnt want to use it to define the constant ... so i renamed the constant as "c" instead. But yes, the textbooks in america tend to use y=mx+b, while i believe the brits use: y = mx+c .... the numbers really dont care what they are named :)

so, let just distribute the slope thru the paranthesis; and add the constants ...
\[y=-2(x+2)+6\]
\[y=-2x+2(-2)+6\]
\[y=-2x-4+6\]
\[y=-2x+2\]

Answer 48

oooh ok, i get you

Answer 49

we could just have easily used some greek letters :)
\[\Large \gamma=\mu\chi+\rho\]

Answer 50

Yes but then i would have been totally lost lol

Answer 51

lol, when the teacher asked what to name the variable, I would ask it to be in celtic runes

Answer 52

the slope-intercept form is defined by its use of the slope (-2), and the "y-intercept" which in our case turns out to be (+2)

Answer 53

ok :) i get you, but you cant be using your big words like Celtic runes, because then i become stuck on dumb llike what?

Answer 54

ill try :) good luck