Question 146377
Equation of line passing through two points ( x1, y1) & (x2, y2) is
  x - x1/x2 - x1 = y - y1 / y2 - y1.

applying above formula in given question

equation of line passing through (5, -2) & (- 3 , 2) is
  x - 5 /-3 - 5 = y - (-2) / 2 - (-2)
 x - 5 /(-8) = y + 2 / 4
cross multiplying, we get

4 ( x - 5) = -8 ( y + 2 )

4x - 20 = -8y -16
4x + 8y -4 = 0, this is the equation of line.

to find the slope,  write the equation in slope -intercept form i.e. y = mx+c.
4x + 8y -4 =0
 8y = - 4x +4
 y = -4x/8 + 4 /8 
 y = -x/2 + 1/2.
this is of slope intercept form,slope  m= -1/2.