Question

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

Answer 1

`2/3`

Explanation:

To find the slope of a perpendicular line we must first find the slope of line given in the problem. To do this we must transform this equation into the slope-intercept format.

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.

Solving the equation in the problem for `y` produces:

`3x - color(green)(3x) + 2y = - color(green)(3x) - 5`

`0 + 2y = -3x - 5`

`2y = -3x - 5`

`(2y)/color(green)(2) = (-3x - 5)/color(green)(2)`

`(color(green)(cancel(color(black)(2)))y)/cancel(color(green)(2)) = -3/2x - 5/2`

`y = color(red)(-3/2)x - color(blue)(5/2)`

Therefore the slope of this line is `color(red)(m) = -3/2`

The slope of a perpendicular line is the negative inverse of the slope of the line we are given, or `color(red)(-1/m)`

So, for our problem the slope of a perpendicular line is `color(red)(- -2/3 = 2/3)`