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

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Answer 1 · 2017-01-07T16:20:36

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

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#