It's a Slippery Slope

Jelly, 23 bytes

Ṛ⁹,2⁶v$Ṡ$e⁵$?¥þị“/ \-”Y

Try it online!

Arguments: Y, X, U, f

f is a Python string containing Jelly code. Be sure to quote it appropriately, otherwise you may encounter errors.

Also, f takes a pair [x, y] as its argument, not two arguments x and y.

2 bytes saved thanks to @ngn

{o←⍺⍺⋄'\-/ '[⊖⍉⍺∘.{0::4⋄2+×⍺o⍵}⍵]}

Try it online! _{(with modified division, since basic APL 0÷0 is 1)}

The black box function comes as left operand, X as left argument, and Y as right argument.

z x=last$0:[x|abs x>1e-9]
(x#y)(%)u=reverse[[last$"\\-/"!!floor(1+signum(z$c%r)):[' '|elem(c,r)u]|c<-x]|r<-y]

Try it online!

Fairly straightforward solution. Uses signum to index into a string for the right char if the point is defined.

EDIT: Thought of a way to shave off a byte

EDIT 2: Thanks @Laikoni for taking off another 4 bytes!