SOLUTION: What is the equation in slope-intercept form of the line through (1,-3) that is perpendicular to y=5?

y = 5 is the equation of a horizontal line.  It should be thought of as

y = 0x + 5

which is an equation in the slope-intercept form:

y = mx + b

So y = 5 is really y = 0x + 5 which has slope 0 and y intercept (0,5).

lines with 0 slope are horizontal since they slope neither uphill to the
right (that is, like this /, i.e. have a positive slope) or dwnhill to 
the right (that is \, i.e., have a negative slope). 
 
Here is the line y = 5 or y = 0x + 5, in green:



Here is the point (1,-3)



Here (in red) is the line through (1,-3) that is perpendicular to the 
green line, which is the line your problem asks for the equation of.



Notice that the red line you want the equation of is vertical.   Vertical 
lines have no slope. Vertical lines which are parallel to the y-axis can have
no y-intercept, since they never intersect it.

The word "intercept" in "slope-intercept form" refers to the y-intercept
only, not the x-intercept.  Therefore the red vertical line has no
slope-intercept form.

However it DOES have an equation, but not a slope-intercept form.

Its equation is determined by looking at other points on the line,
and writing what is true about them.  Look at all these other
points on that red vertical line?




There is one thing and only one thing that can be said about
every one of those points on that red vertical line, and that is:

     THEIR x VALUES ARE ALL 1.

Therefore the only equation that describes that vertical line
is this simple equation:

              x = 1

That is the equation of the red vertical line.  However it
is NOT a slope-intercept form.   Vertical lines are the only
kinds of lines that have neither slopes not y-intercepts.  The
only kinds of equations they can have are this kind:

              x = ↏

where there is some number, positive, negative or zero in the box.

Edwin