The formula for find the slope of a line is:
#m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#
Where #(color(blue)(x_1), color(blue)(y_1))# and #(color(red)(x_2), color(red)(y_2))# are two points on the line.
Substituting the values from the points in the problem gives:
#m = (color(red)(5/2) - color(blue)(-3))/(color(red)(-5) - color(blue)(-7/2))#
#m = (color(red)(5/2) + color(blue)(3))/(color(red)(-5) + color(blue)(7/2))#
#m = (color(red)(5/2) + color(blue)((2/2 xx 3)))/(color(red)((2/2 xx -5)) + color(blue)(7/2))#
#m = (color(red)(5/2) + color(blue)(6/2))/(color(red)(-10/2) + color(blue)(7/2))#
#m = (11/2)/(-3/2)#
#m = (11 xx 2)/(-3 xx 2)#
#m = -22/6#
#m = -11/3#