Question 240825
find the slope. through (4,-2) and parallel to x=1
<pre>
That's a vertical line, and it has NO slope!

All equations of the form 

x = a

are vertical lines which are " a " units from the y-axis.

The vertical line whose equation is x = 1 is this green
line below:

{{{drawing(400,400,-5,5,-5,5,
graph(400,400,-5,5,-5,5),
green(line(1,-6,1,6)) )}}}

The point (4,-2) is this point plotted below:

{{{drawing(400,400,-6,6,-6,6,
graph(400,400,-6,6,-6,6),
green(line(1,-7,1,7)),

line(4+.1,-2,4-.1,-2), line(4,-2+.1,4,-2-.1),line(4+.1,-2+.1,4-.1,-2-.1),line(4+.1,-2-.1,4-.1,-2+.1), locate(4.2,-2,"(4,-2)") 

 )}}}

The line parallel to the vertical line whose
equation is x = 1 which goes through the point
(4,-2) is the blue vertical line below:

{{{drawing(400,400,-6,6,-6,6,
graph(400,400,-6,6,-6,6),
green(line(1,-7,1,7)),

line(4+.1,-2,4-.1,-2), line(4,-2+.1,4,-2-.1),line(4+.1,-2+.1,4-.1,-2-.1),line(4+.1,-2-.1,4-.1,-2+.1), locate(4.2,-2,"(4,-2)"), 
blue(line(4,-7,4,7))  )}}}

Its equation is x = 4.  But neither line has a slope.
Vertical lines are the only kind of lines which have no slope.
All other lines have slopes.

Edwin</pre>