Answer
$\dfrac{3}{11}$
Work Step by Step
Formula to calculate the slope of points:
$m=\dfrac{x-x_0}{y-y_0}$
Here, $(x_0,y_0)=(5,-4)$ and $(x,y)=(2,7)$
Thus,
$m=\dfrac{x-x_0}{y-y_0}=\dfrac{7-(-4))}{2-5}=-\dfrac{11}{3}$
Since, the slopes of two perpendicular lines will be opposite reciprocals.
Hence, $m=-\dfrac{1}{-\dfrac{11}{3}}=\dfrac{3}{11}$
