Question

What is the slope of a line perpendicular to the line whose equation is y= -2/3x -5

Answer 1

`(3)/(2)`

Explanation:

Hi there!

In the given equation,
`y= -(2)/(3) x -5`, the slope of the line is
`-(2)/(3)`.

Perpendicular lines always have slopes that are negative reciprocals, like negative "flipped" fractions.

Example: The reciprocal of
`(2)/(1)` (which is the same as 2) is
`(1)/(2)`. The negative of
`(1)/(2)` is
`-(1)/(2)`.

Example 2: The negative reciprocal of
`-(4)/(3)` is
`(3)/(4)`.

Using this logic, we can determine that the negative reciprocal of
`-(2)/(3)` is
`(3)/(2)`. Therefore, the slope of a line perpendicular to the line whose equation is
`y= -(2)/(3) x -5` would be
`(3)/(2)`.

I hope this helps!