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

1 Answer
Dec 26, 2016

Answer:

#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)#