Algebra 1

$\dfrac{3}{11}$
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, $m=-\dfrac{1}{-\dfrac{11}{3}}=\dfrac{3}{11}$