Explain why the slope of a vertical line is referred to as undefined

Question

solomonzelman · Answer

Plug any two points of any vertical line into a slope formula, and find out.

genny7 · Answer

I dont know how to do that

anonymous · Answer

coz formula to find slope=y=x

and a verticale line has x coordinate=0

so by putting x=0 here what you will get..???that is infinity..

solomonzelman · Answer

Let say you have a line  x=4. Choose any 2 points, lets say, you choose (4,5) and (4,6) .

$\Large\color{blue}{    \frac{y_1-y_2}{x_1-x_2} =\frac{5-6}{4-4} = \frac{-1}{0} =undefined }$

genny7 · Answer

@SolomonZelman ohhh now i understand does that happen very often in equations?

solomonzelman · Answer

This happens whenever you have a slope of vertical line (at least).

The reason for this is because the denominator of the slope formula is (x1-x2) and all x-coordinates of the line are the same, so x1 and x2 are the same, and thus the denominator will always be zero.

genny7 · Answer

Oh okay thanks sooo much!!! @SolomonZelman

solomonzelman · Answer

YW

genny7 · Answer

:)