# Separable Equations help

## Homework Statement

Find the y-intercept of the curve that passes through the point (4/9,1) and whose slope at (x,y) is −2/y3.

## The Attempt at a Solution

woudnt the y-int be y=-2x/y3 + 5.5 ?
i got it by plugging the slope into m in the equation y=mx+b
then plugged in the given points to get b..
but the question wants a numerical solution :S

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gabbagabbahey
Homework Helper
Gold Member
i got it by plugging the slope into m in the equation y=mx+b
That's the equation of a straight line, with constant slope, $m$. The slope you are given isn't constant, it depends on $y$. Your curve is not a straight line.

What is the slope of any curve $f(x)$ at the point $(x,f(x))$?...Use that.

Dick
Homework Helper
That makes no sense whatsoever. I think you know that. They want the y intercept of the curve. I think you have to solve for the curve. Whatever happened to the "separable equations" part of your post title? Shouldn't you separate dy/dx=(-2/y^3) and solve it??

That makes no sense whatsoever. I think you know that. They want the y intercept of the curve. I think you have to solve for the curve. Whatever happened to the "separable equations" part of your post title? Shouldn't you separate dy/dx=(-2/y^3) and solve it??
okay so i get dy/dx=(-2/y^3)
==> y^3 dy = -2dx
==> (y^4)/4 = -2x + C
==> y= sqrt4(-8x + 4C)

now what do i do?

rock.freak667
Homework Helper
okay so i get dy/dx=(-2/y^3)
==> y^3 dy = -2dx
==> (y^4)/4 = -2x + C
==> y= sqrt4(-8x + 4C)

now what do i do?
They gave you a point that it passes through, so find, the constant C.

They gave you a point that it passes through, so find, the constant C.
well if i plug (9/4, 1) in, i get C=4.75
from there y= sqrt4(-8x + 19)
now what do i do with this?

Office_Shredder
Staff Emeritus
Gold Member
So you have a curve passing through the point given, with the slope that they require. What does the question tell you to do with it?

So you have a curve passing through the point given, with the slope that they require. What does the question tell you to do with it?
i got 2.087
once i got y = (-8x + 19)^0.25
y-int is when x=0 so y=19^0.25 = 2.087

its weird how the slope they gave us dont even help.. its there to make the question scary i guess.

Office_Shredder
Staff Emeritus