Question

How do you find the slope of the line that passes through (-8,6), (-8,4)?

Answer 1

slope is undefined.

Explanation:

One way is to use the `color(blue)"gradient formula"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`
where m represents the slope and `(x_1,y_1),(x_2,y_2)" 2 points on the line"`

The 2 points here are (-8 ,6) and (-8 ,4)

let `(x_1,y_1)=(-8,6)" and " (x_2,y_2)=(-8,4)`

`rArrm=(4-6)/(-8-(-8))=(-2)/0`

Division by zero makes m undefined, hence slope is undefined.

Another way is to note that the x-coordinates of the 2 points are equal, that is both - 8
This indicates that the line is vertical and parallel to the y-axis, passing through all points in the plane with an x-coordinate of
- 8. The equation of the line is x = - 8 and since it is vertical has an undefined slope.
graph{y-1000x-8000=0 [-10, 10, -5, 5]}