Question

What is the slope of the line perpendicular to `y=-5/3-6`?

Answer 1

As asked `y=-5/3-6=-23/6` is a horizontal line; any line perpendicular to it would be vertical and thus have an undefined slope.
If the intended equation was `y=-5/3color(blue)x-6`
see below.

Explanation:

Any equation in the form `y=color(green)mx+b` is in slope-intercept form with a slope of `color(green)m`

If a line has a slope of `color(green)m`
then all lines perpendicular to it have a slope of `-(1/color(green)m)`

If the equation was intended to be
`color(white)("XXX")y=color(green)(-5/3)x-6`
then all lines perpendicular to it will have a slope:
`color(white)("XXX")-(1/(color(green)(-5/3)))=color(magenta)(3/5)`

Answer 2

`"slope "=3/5`

Explanation:

`"assuming "y=-5/3x-6" is meant"`

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`y=-5/3x-6" is in this form with "m=-5/3`

`"given a line with slope m then the slope of a line"`
`"perpendicular to it is"`

`•color(white)(x)m_(color(red)"perpendicular")=-1/m`

`rArrm_(color(red)"perpendicular")=-1/(-5/3)=3/5`