Question

Find the slope of the line containing the given pair of points. If the line is undefined, state so. Please be sure to show all of your work.

(-1, -3) and (-1, -5)

Answer 1

both points have the same abscissa then they belongs to a vertical line
then the slope is undefined

Answer 2

usually the line is 'undefined' because the gradient is undefined, as in this case:\[\frac{-5+3}{-1-(-1)} = -2/0\] is the gradient - but you cannot divide by zero! In fact, the gradient of this line is \[\lim_{x\rightarrow 0}\frac{-2}{x} = -\infty\]