How do I find all line through (, -1) for which the product of the x- & y- intercepts is 3?
You forgot the x value of your given point.
I will insert an arbitrary value of 2, give you a solution and then you can follow that method for your correct point.
Let the equation be y = mx + b
but the point (2,-1) is on it, so
-1 = 2m + b
b = -1/(2m)
the equation would then be
y = mx - 1/(2m)
y-intercept is -1/(2m)
x-intercept: let y=0 ---> x =1/(2m^2)
given: (-1/(2m))*(1/(2m^2)) = 3
12m^3 = -1
m = -1/cuberoot(12)
put that back in y = mx - 1/(2m)