Question

Find the slope of the line through the psi of points A(2, -3), p(2,9)

Answer 1

The slope of a line passing through two points is the ratio between the difference of the y coordinates and the difference of the x coordinates. In formulas, you have

$m(A,B) = \cfrac{\Delta y}{\Delta x} = \cfrac{A_y-B_y}{A_x-B_x}$

If you plug your values, you have

$m(A,B) = \cfrac{\Delta y}{\Delta x} = \cfrac{-3-9}{2-2} = \cfrac{-12}{0}$

which is undefined.

In fact, since the two points share the same x coordinate, the segment AB is vertical, and the slope is not defined for vertical lines.