This is a vertical line, which is the only case where 
there is no slope-intercept form.  However there is an
equation for it.

Let's begin by drawing the line whose equation is y = 5.
I'll draw it green.  I'll also plot the point (-4,1)





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Now we'll draw a blue line through (-4,1) which is perpendicular 
to the green line  



The way to determine its equation is to look at several points
on that blue vertical line and to observe what one thing is true about
all of them:

Lets look at some points on that blue vertical line:



Notice what all those points

(-4,5), (-4,3), (-4,1), (-4,-3), (-4,-5), (-4,-8)

have in common.  They all have their x-coordinates

equal to -4.  So all we do is write that the x
value on every point on that line is -4, and to do that
we simply write the simple equation

x = -4 

That equation is only true for points on that line,
so that is the equation of the blue vertical line.  There
is no slope-intecept for it because there is no "m",
because vertical lines do not have a slope.  There is
also no "b" because vertical lines have no y-intercept.

So the only thing we can do is write the simple equation
which describes every point on that blue vertical line, which
is x = -4.

Edwin