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

Parallel lines have equal slopes. Therefore, the slope of the required line is equal to the slope of the line passing through $(4,-2)$ and $(-3,5)$.The formula for the slope ($m$) of a line passing through $(x_1,y_1)$ and $(x_2,y_2)$ is:
$$m=\frac{y_2-y_1}{x_2-x_1}$$
Substitute the given points $(x_1,y_1)=(4,-2)$ and $(x_2,y_2)=(-3,5)$:
$$m=\frac{5-(-2)}{-3-4}$$
$$m=\frac{5+2}{-7}$$
$$m=\frac{7}{-7}=-1$$
Since the lines are parallel, the required slope is also $-1$.