The problem involves finding the y-intercept of a curve that passes through the point (4/9, 1) and has a slope defined by the expression -2/y³. The discussion centers around understanding the nature of the curve and the implications of the given slope.
The discussion is active, with participants exploring different interpretations of the problem. Some have derived a potential equation for the curve and are questioning how to use it to find the y-intercept. There is no explicit consensus on the final approach, but guidance has been offered regarding the use of the point provided in the problem.
Participants note the requirement to find a numerical solution for the y-intercept, while also grappling with the implications of the slope's complexity. There is mention of the need to solve for the curve before determining the y-intercept.
Slimsta said:i got it by plugging the slope into m in the equation y=mx+b
Dick said: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 said: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 said:They gave you a point that it passes through, so find, the constant C.
Office_Shredder said: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?