What is the slope of x=3?

1 Answer
Jun 10, 2015

It is a degenerated case becausex=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.