Question

How do you find the slope of `(12, 10), (12, 5)`?

Answer 1

slope is undefined.

Explanation:

To calculate the slope (m) use the `color(blue)"gradient formula"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(a/a)|)))`
where `(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points"`

The 2 points here are (12 ,10) and (12 ,5)

let `(x_1,y_1)=(12,10)" and " (x_2,y_2)=(12,5)`

`rArrm=(5-10)/(12-12)=(-5)/0`

Division by 0 is undefined , hence slope is undefined.

This is, in fact, a line parallel to the y-axis and passing through all points in the plane with an x-coordinate equal to 12.
For this reason it's equation is x = 12

A 'quick' way to note when this situation occurs is to observe that the x-coordinates of the 2 given points are equal.
graph{y-1000x+12000=0 [-20, 20, -10, 10]}