Question

What is the slope of the line that is parallel to the y-axis and passes through the point (–1, 5)?

Answer 1

What is the slope of the line that is parallel to the y-axis and passes through the point (–1, 5)?

check the picture below.

the y-axis is a vertical line, thus any line parallel to it, will also be a vertical line, so, let's pick another point, hmmmmm say -1, 3, thus

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -1 &,& 5~) % (c,d) &&(~ -1 &,& 3~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-5}{-1-(-1)}\implies \cfrac{3-5}{-1+1}\implies \stackrel{und efined}{\cfrac{-2}{0}}$

Answer 2

Undefined because the slop of the y axis is undefined