We first plot those two points and draw a line 
through them to find out if it is vertical or
not. The equations of all lines can be placed
in slope-intercept form except the equations
for vertical lines. This is the graph we get:



We see that it is not vertical. So we can proceed
as usual:

We are to find an equation of the line containing 
the points (-1,3) and (4,-2)

Use the slope formula:

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

where (x1, y1) = (-1,3) and (x2, y2) = (4, -2)

    (-2) - (3)    -5      -5
m = —————————— = ————— = ———— = -1
    (4) - (-1)    4+1      5 

Now substitute in the point slope formula:

   y - y1 = m(x - x1)

   y - 3 = (-1)(x - (-1) )

   y - 3 = -(x + 1)

   y - 3 = -x - 1

       y = -x + 2

That's the equation in the slope-intercept
form because we can compare it with

       y = mx + b

and see that its slope m is -1 and its
y-intercept (0,b) is the point (0,2)
  

As before we first plot those two points and 
draw a line through them to find out if it is
vertical or not. The equations of all lines 
can be placed in slope-intercept form except
the equations for vertical lines.
This is the graph we get:



We see that it is vertical.  That means we
cannot proceed as above to find its equation.
However it is very easy because we see that
every point on the vertical line is either
directly above or directly below the point
on the x-axis where x = 2,

So that's its equation:

     x = 2

[The equations of vertical lines are always
 of the simple form

     x = a

where a is the number on the x-axis where the
vertical line cuts through at.]

Edwin