tangent lines to the curve y = x^3 that intersect (0,-16)

[tdotgirl]

i don't know how to do this:

find the equation of all tangent lines to the curve y = x^3 that intersect (0,-16)

all i know so far is:
the slope of the line is 3x^2. the line intersects a point on x^3 and (0, -16).

is this correct? how do i get the equation of the line?

 

[skeeter]

every point on the curve y = x^3 has coordinates (x, x^3).

all lines that touch the curve and pass through the point (0, -16) have slope

m = [x^3 - (-16)]/(x - 0) = (x^3 + 16)/x

the slope of all lines tangent to the curve y = x^3 have slope, m = 3x^2

now ... what do you think you should do with the two expressions that define the slopes?