Question 465569
You have to have {{{-kx - 9 = x^2 - 2x}}}

<==> {{{x^2 + (k+2)x + 9 = 0}}}

For non-intersection, the discriminant should be < 0.

Whence  {{{(k-2)^2 - 4*1*9 <0}}}

==> {{{k^2 - 4k - 32 <0}}}

<==> (k-8)(k + 4) < 0  ==> the solution set is the interval (-4,8)

Hence as long as k{{{epsilon(-4,8)}}}, the line and the parabola won't intersect.