Find the equation of the line tangent to x^5 = -xy^3 at (1,-1) Put it in slope-int. form?

Question

anonymous · Answer

you just found the derivative right?

anonymous · Answer

think so... I can't figure out how to put it in y=mx+b form

anonymous · Answer

you need $m$ first
replace $x$ by $1$ and $y$ by $-1$ in the derivative to find $m$
then use the point - slope formula

anonymous · Answer

So, 1^(5) = -(1)(-1)^3 ? I might not figure this one out

anonymous · Answer

no not in the equation, in the derivative you found

anonymous · Answer

im so confused.

anonymous · Answer

k lets go slow

anonymous · Answer

i can't remember the derivative exactly, but i think it was 
$$y'=-\frac{5x^4+y^3}{3xy^2}$$ is that right?

anonymous · Answer

x^5 = -xy^3

anonymous · Answer

the derivative you found earlier, not the original equation

anonymous · Answer

hey satellite can you back when you're done here? I have a question on another problem for you

anonymous · Answer

I trust your backing mate.

anonymous · Answer

it was $$y'=-\frac{5x^4+y^3}{3xy^2}$$

anonymous · Answer

ah, yes

anonymous · Answer

now put $x=1,y=-1$ in to the derivative

anonymous · Answer

you get 
$$m=-\frac{5-1}{3}=-\frac{4}{3}$$ if my arithmetic is right

anonymous · Answer

that is the slope, the point is $(1,-1)$ and use the point slope formula to find the equation of the line

anonymous · Answer

so, the answer comes out to be -4/3 cause of that right?

anonymous · Answer

that is what i get for the slope, yes

anonymous · Answer

is there even a +b to the y= mx+b of it?

anonymous · Answer

It has to be formal

anonymous · Answer

you lost me there

anonymous · Answer

$$y+1=-\frac{4}{3}(x-1)$$ and then put it in any form

anonymous · Answer

I have to put the eq. of the line tangent to x^5 = -xy^3 at (1,-1). Then, i gotta put it in slope-intercept form (y = mx + b)

anonymous · Answer

this is the point slope form 
$$y+1=-\frac{4}{3}(x-1)$$ if you want it in the form $y=mx+b$ then solve for $y$

anonymous · Answer

y = -4/3x + 1, right? i am terr. at math. ;)

anonymous · Answer

lol no
multiply first

anonymous · Answer

y + 1 = -4/3x + 4/3x

anonymous · Answer

$$y+1=-\frac{4}{3}(x-1)\
y+1=-\frac{4}{3}x+\frac{4}{3}$$ then subtract $1$ and get 
$$y=-\frac{4}{3}x+\frac{1}{3}$$

anonymous · Answer

You work miracles like no other mate. im startin' to get the gist of this

anonymous · Answer

good!
yw