What is the slope of the line perpendicular to the line passing through the points $(-4,5)$ and $(3,-2)$?

1. Find the slope ($m_1$) of the line passing through the points $(x_1,y_1)=(-4,5)$ and $(x_2,y_2)=(3,-2)$:
$$m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-5}{3-(-4)}=\frac{-7}{7}=-1$$
Let $m_2$ be the slope of the line perpendicular to this line. The product of the slopes of two perpendicular lines is $-1$:
$$m_1\times m_2=-1$$
$$(-1)\times m_2=-1$$
$$m_2=1$$
Therefore, the slope of the perpendicular line is $1$.