I'm learning how to write my "results" in 
slope-intercept form. And I'm having a little
difficulty trying to get these worked out and 
was wondering if I could get some assistance. 

(0,5), m =  

Substitute in the point slope formula:

   y - y1 = m(x - x1)

where x1 = 0 and y1 = 5

   y - 5 = (x - (0) )

   y - 5 = x

       y = x + 5

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  and its
y-intercept (0,b) is the point (0,5)

---------------------------------------

1. (-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)
  
---------------------------------------

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

We plot those two points and draw a line
through them:



It is vertical, so we can't go the usual route.
Since vertical lines are the only kind of lines
which don't have slopes, there is no slope-intercept
form.  But we can still write the equation.  It is 
simply this:

       x = 2

because every point on that line has x-coordinate 2.

So x = 2 tells the story of every point on the line,
so that's all there is to the equation of that vertical
line.

Edwin