Question

Find the slope of the line through the pair of points. A(2, –3), P(2, 9)

Answer 1

The slope: $m=\dfrac{y_2-y_1}{x_2-x_1}$

$A(2;-3)\to x_1=2;\ y_1=-3\\P(2;\ 9)\to x_2=2;\ y_2=9\\\\subtitute:\\\\m=\dfrac{9-(-3)}{2-2}=\dfrac{12}{0}!!!$

The denominator can not be zero!

Conclusion: The slope is undenfined.

Answer 2

We are given with two points and is asked for the slope of the line formed by the two points. The formula of the slope is equal to change in y over change in x. In this case, the slope is (9+3)/(2-2) equal to 12/0 equal to infinity. This means the line connecting the two is a vertical line