Question

What is the slope of any line perpendicular to the line passing through `(-6,-4)` and `(7,-12)`?

Answer 1

The perpendicular slope would be `m=13/8`

Explanation:

The slope a line that is perpendicular to a given line would be the inverse slope of the given line

`m = a/b` the perpendicular slope would be `m =-b/a`

The formula for the slope of a line based upon two coordinate points is

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

For the coordinate points `(-6,-4) and (7,-12)`
`x_1 = -6`
`x_2 = 7`
`y_1 = -4`
`y_2 = -12`

`m = (-12-(-4))/(7-(-6))`

`m = -8/13`

The slope is `m = -8/13`
the perpendicular slope would be the reciprocal (-1/m)
`m = 13/8`