Question

What is the slope of the line perpendicular to `y=2/3x-6`?

Answer 1

Slope of the line perpendicular to `y` is `-3/2`
See a solution process below:

Explanation:

The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

`y = color(red)(2/3)x - color(blue)(6)`

Therefore, the slope of the line represented by the equation in the problem is:

`color(red)(m = 2/3)`

Let's call the slope of a perpendicular line: `m_p`

The slope of a perpendicular line is:

`m_p = -1/m`

Substituting gives:

`m_p = -1/(2/3) = -3/2`