Solve for the y-Intercept: Curve Through (4/9,1) with Slope of -2/y3

[Slimsta]

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.

Homework Equations

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

 

[gabbagabbahey]

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]

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??

 

[Slimsta]

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]

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.

 

[Slimsta]

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]

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?

 

[Slimsta]

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 don't even help.. its there to make the question scary i guess.

 

[Office_Shredder]

You used the slope to figure out what y was as a function of x. How can you plug in x=0 if you don't know what the function is?