Question

How do you find the slope that is perpendicular to the line `y=-2/3x -5`?

Answer 1

`3/2`

Explanation:

If `color(blue)(L_1)` has a slope of `color(blue)(m)`
and
if `color(red)(L_2)` is perpendicular to `color(blue)(L_1)`
then
`color(red)(L_2)` has a slope of `color(red)(-1/m)`

The equation `y=color(blue)(-2/3)x-5`
is in slope-intercept form with a slope of `color(blue)(m=-2/3)`

Therefore any line perpendicular to it has a slope:
`color(white)("XXX")color(red)(-1/(""(color(blue)(-2/3))))=color(red)(3/2)`