Question

Question #ec492

Answer 1

The slope is `22/89`

Explanation:

Differentiate:

`8x + 4y + 4xdy/dx + 6y^2dy/dx = 0`

Move all of the terms without `dy/dx` to the right:

`4xdy/dx + 6y^2dy/dx = -8x - 4y`

Factor out `dy/dx` on the left:

`(4x + 6y^2)dy/dx = -8x - 4y`

Divide both sides by `(4x + 6y^2)`:

`dy/dx = (-8x - 4y)/(4x + 6y^2)`

Remove a common factor of `2/2`:

`dy/dx = (-4x - 2y)/(2x + 3y^2)`

The slope, m, is the above evaluated at `(-7,-8)`

`m = (-4(-7) - 2(-8))/(2(-7) + 3(-8)^2)`

`m = (44)/(178) = 22/89`