Question

How do you find the slope given (c, d) and (c, 1/d)?

Answer 1

The slope is undefined and the line is a vertical line through `x` at `c`
Whenever the `x` value of two points of a line are the same value the slope is undefined.

Explanation:

Slope which is the change in `x` versus the change in `y`.

Slope is identified by the letter `m`

`m = (Deltay)/(Deltax)`

`m=(y_2-y_1)/(x_2-x_1)`

`(c,d)` and `(c,1/d)`

`x_1=c`
`y_1=d`
`x_2=c`
`y_2=1/d`

`m = (1/d-d)/(c-c)`

`m = (1/d-d/d)/(c-c)`

`m = ((1-d)/d)/(0)`

Because the numerator is `0` this fraction is undefined

`m =` undefined

The slope is undefined and the line is a vertical line through `x` at `c`
Whenever the `x` value of two points of a line are the same value the slope is undefined.