What is the slope of #x=3#?

1 Answer
Jun 10, 2015

Answer:

It is a degenerated case because#x=3# is not a function. The slope doesn't exist, but we can say that it tends to infinite (#m->oo#).

Explanation:

#x=3# is not a function (there isn't any y, to keep it simpe).
If you take the common line function in space you have:
#y=mx+q# where #m# is the slope.
If you imagine to grow m to infinite you can obtain an almost vertical line. For example see the graph of #y=10000x+10000#:

graph{y=10000x+10000 [-10, 10, -5, 5]}

Anyway #x=k# is a very peculiar case. If you use the common formula to obtain the slope for example for the two points #A(3,0) and B(3,5)# of the line you get this fraction:
#Delta_Y/Delta_X=(5-0)/(3-3)=5/0.#
Obviously this fraction doesn't make sense because it's a particular case.
For this reasons, some people say that #m=oo# but it is formally wrong, they should say that #m->oo# because m doesn't exist.