Question 271957
I have to write the slope-intercept form equation of the line described:

Y = 5 is a zero slope so I don't know where to go from here. Can you guide me through this?

Thanks

through (-4,1) perpendicular to y = 5.
<pre><font size = 4 color = "indigo"><b>
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)

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
green(line(-11,5,11,5))
line(-4+.1,1,-4-.1,1), line(-4,1+.1,-4,1-.1), line(-4+.1,1+.1,-4-.1,1-.1), line(-4+.1,1-.1,-4-.1,1+.1),locate(-3.7,1.4,"(-4,1)") )}}}



 )}}}
 

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

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
green(line(-11,5,11,5)), blue(line(-4,11,-4,-11)),
line(-4+.1,1,-4-.1,1), line(-4,1+.1,-4,1-.1), line(-4+.1,1+.1,-4-.1,1-.1), line(-4+.1,1-.1,-4-.1,1+.1),
locate(-4+.3,1.4,"(-4,1)")

 )}}}

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:

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
green(line(-11,5,11,5)), blue(line(-4,11,-4,-11)),
line(-4+.1,1,-4-.1,1), line(-4,1+.1,-4,1-.1), line(-4+.1,1+.1,-4-.1,1-.1), line(-4+.1,1-.1,-4-.1,1+.1),
locate(-4+.3,1.4,"(-4,1)"),

line(-4+.1,3,-4-.1,3), line(-4,3+.1,-4,3-.1), line(-4+.1,3+.1,-4-.1,3-.1), line(-4+.1,3-.1,-4-.1,3+.1),
locate(-4+.3,3+.4,"(-4,3)"),

line(-4+.1,5,-4-.1,5), line(-4,5+.1,-4,5-.1), line(-4+.1,5+.1,-4-.1,5-.1), line(-4+.1,5-.1,-4-.1,5+.1),
locate(-4+.3,5+.4,"(-4,5)"),


line(-4+.1,-3,-4-.1,-3), line(-4,-3+.1,-4,-3-.1), line(-4+.1,-3+.1,-4-.1,-3-.1), line(-4+.1,-3-.1,-4-.1,-3+.1),
locate(-4+.3,-3+.4,"(-4,-3)"),

line(-4+.1,7,-4-.1,7), line(-4,7+.1,-4,7-.1), line(-4+.1,7+.1,-4-.1,7-.1), line(-4+.1,7-.1,-4-.1,7+.1),
locate(-4+.3,7+.4,"(-4,1)"),

line(-4+.1,-8,-4-.1,-8), line(-4,-8+.1,-4,-8-.1), line(-4+.1,-8+.1,-4-.1,-8-.1), line(-4+.1,-8-.1,-4-.1,-8+.1),
locate(-4+.3,-8+.4,"(-4,-8)"),


line(-4+.1,-5,-4-.1,-5), line(-4,-5+.1,-4,-5-.1), line(-4+.1,-5+.1,-4-.1,-5-.1), line(-4+.1,-5-.1,-4-.1,-5+.1),
locate(-4+.3,-5+.4,"(-4,-5)")  )}}}

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</pre>