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The slope of the first line is $\dfrac{4-(-4)}{5-(-7)} = \dfrac{8}{12} = \dfrac{2}{3}$.
The slope of the second line is $\dfrac{(-9)-6}{6-(-4)} = \dfrac{-15}{10} = -\dfrac{3}{2}$.
Since $\dfrac{2}{3} \neq -\dfrac{3}{2}$, the two lines are $\boxed{\text{neither}}$ parallel nor perpendicular.