SOLUTION: write the equation of the line passing through each of the given pairs of points. write result in slope-intercept form, where possible.

You forgot to give the two points.
Let's say they are these points:

(-1, 3) and (4,-2)

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)
  
--------------------------------------

If the two points had been (4,-5) and (4,3)
we would have gotten this vertical line:



and its equation would have simply been

      x = 4

because every point on it has 4 for 
its x-coordinate.

Edwin