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

1 Answer
Jan 7, 2017

Answer:

Convert to the slope-intercept form and then, using the slope from this form of the equation, take the negative inverse of the slope.

Explanation:

First, we need to find the slope of the line given in the problem. To do this we need to put this equation in the 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.

We can convert the equation from our problem to this form by solving for #y#:

#5x - 3y = 2#

#5x - color(red)(5x) - 3y = - color(red)(5x) + 2#

#0 - 3y = - color(red)(5x) + 2#

#-3y = -5x + 2#

#(-3y)/color(red)(-3) = (-5x + 2)/color(red)(-3)#

#(color(red)(cancel(color(black)(-3)))y)/cancel(color(red)(-3)) = (-5x)/color(red)(-3) + 2/color(red)(-3)#

#y = 5/3x - 2/3#

The slope of this line is #m = 5/3#

For any line with slope #color(red)(m)# any line perpendicular to this line will have the negative inverse of the original line or #-1/color(red)(m)#

Therefore the slope of a line perpendicular to the line in the problem will be:

#-3/5#