Write an equation in slope intercept form 
for the line passing through the pair of points
 (-1,3) and (2,-5)

First use the equation for the slope:

     y2 - y1
m = —————————
     x2 - x1

where (x1, y1) = (-1, 3) and (x2, y2) = (2, -5)

      (-5) - (3)      -5 - 3     -8
m = —————————————— = ———————— = ———— = -8/3
      (2) - (-1)       2 + 1      3 

Now substitute in the point slope formula:

y - y1 = m(x - x1)

y - 3 = (-8/3)( x - (-1) )
y - 3 = (-8/3)(x + 1)
y - 3 = (-8/3)x - 8/3

Multiply both side by LCD = 3

  3y - 9 = -8x - 8

 8x + 3y = 1

That's the answer in standard form. If you
need it to be in slope-intercept form, solve
it for y:

     3y = -8x + 1

      y = (-8/3)x + 1/3

Edwin