write the equation of the line in point-slope form. (-2,4) and (-5,6). i found the slope, it is 2/-3.

- anonymous

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- anonymous

I am looking for the y-intercept so this is what i have so far:

- anonymous

y= mx+b
4= 2/-3(-2)+b

- anonymous

then its 4= -4/-3 +b no idk what to do

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- anonymous

this site helps sometimes try it http://www.wolframalpha.com/

- anonymous

but if you want an explanation ask someone

- anonymous

it gave me 4= b+ 4/3 which is 8/3

- anonymous

now how do i use the slope 2/-3 and b which is 8/3 to make an equation of the line in point-slope form

- ivettef365

ok you have
4 = -2/3 (-2) + b
4 = 4/3 + b
4 4 12 -4 8
-- - --- = ----- = ------
1 3 3 3
so b = 8/3

- ivettef365

now just plug in on formula y = mx + b
y = -2/3x + 8/3

- anonymous

noo i need point slope formula.

- anonymous

"2.Determine the equation of the line in point-slope form"

- ivettef365

y - y1 = m(x - x1) (this formual ?)

- anonymous

yes

- ivettef365

then you have m = -2/3 and (x,y) could be any known point
you have point (-2,4)
so it is y - 4 = -2/3(x + 2)

- anonymous

so.. y-4= -2/3 x then what

- phi

If they want point - slope form, you do not need to first find y= mx + b (slope-intercept form)
instead, find the slope, which you did
and then pick one of the points, and use that point in
\[ y - y_1= m(x-x_1) \]

- anonymous

y-4= -2/3 x + -4/3 right?

- anonymous

ohh so i did an extra step woops

- phi

Don't distribute. point-slope form is just
\[ y - y_1= m(x-x_1) \]
leave it that way

- anonymous

ohh

- anonymous

r u sure

- ivettef365

is just y - 4 = -2/3(x + 2)

- ivettef365

http://www.mathsisfun.com/algebra/line-equation-point-slope.html

- anonymous

y - y1 = m(x - x1)
do not distribute...just leave it , parenthesis and all

- anonymous

ok

- anonymous

i have a few more questions im gonna put the next one

- phi

point-slope form is not very useful (for plotting for example) but it is easier to write down (less algebra).

- anonymous

yes

- anonymous

my next one is Determine the equation of the line, in slope-intercept form

- anonymous

the points are:

- anonymous

(-5,6) and (-8,8)

- phi

this one is y = mx + b
which you have done already
first find the slope,
then solve for b

- anonymous

for slope i got 2/-3

- anonymous

so i plug in a point, and the slope, to solve for b?

- phi

yes

- anonymous

ok ill use (-5,6)

- anonymous

ok i got 6= -10/-3 +b

- anonymous

so that's like the same as 6= 10/3 +b right

- phi

yes. now add -10/3 to both sides

- anonymous

10/3 u mean

- phi

6= 10/3 +b
add -10/3 to both sides

- phi

because you want 10/3 - 10/3 = 0 so you get 0+b on the right side

- anonymous

wait wait ur confusing me, look what ur writing. first u write 10/3 then u write -10/3.. which is it?

- phi

here is what you did:
ok i got 6= -10/-3 +b
so that's like the same as 6= 10/3 +b right
yes, that is correct:
6 = 10/3 + b
now to solve for b, add -10/3 to both sides

- anonymous

see u did it again

- anonymous

u wrote "now to solve for b, add -10/3 to both sides" do u see the problem here?

- anonymous

but just before you wrote 6= 10/3 +b

- anonymous

y would i add -10/3 to both sides if we just made the fraction simpler by taking away the negatives?

- anonymous

do i add or subtract

- anonymous

if would have been less confusing if u said subtract 10/3 from both sides

- anonymous

so now whats 6 - 10/3 ?

- phi

you agree we started with
y = - 2/3 x + b
you picked point (-5,6) and got
6 = - 2/3 * -5 + b which becomes
6 = 10/3 + b
so far, so good.
now add -10/3 to both sides. Can you do that ?

- phi

to do fractions, you need a common denominator. in this case, 3
to get a denominator of 3 for 6, multiply 6 times 3/3
you get 18/3
now you can do the fractions

- anonymous

so b is 18/3 ??

- phi

you should get
b= 6 - 10/3
change 6 to 18/3
b= 18/3 - 10/3
to add or subtract fractions with the same bottom, add or subtract the tops
18 -10 = 8
and put that number over the common denominator

- anonymous

so 8/3

- phi

yes

- phi

It looks like all the points are ending up on the same line
y= -2/3 x + 8/3 looks familiar

- anonymous

yup

- anonymous

because they are. i made it that way

- anonymous

we had to pick three points and make them be in the same line as (1,2) the "launch area" for a project.

- phi

and then you have to find the different ways to write an equation of a line: standard, point-slope, point-interecept ?

- anonymous

yes

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