What is the slope of a line that is perpendicular to #3y+2x=6#?

2 Answers
Dillon B.
Apr 2, 2018

#m=3/2#

Explanation:

A line is a negative inverse of it perpendicular line.
This means m(1) #m(1)=-1/(m(2))#

Through manipulation of the equation we change it to #y=-2/3x+6/3#
The #-2/3# infront of the represents the slope of the line.
Using idea from earlier we flip the gradient and times it by -1.
#-2/3=-1/m # (cross multiply)

#3m=2# (divide the 3)

#m=3/2#

Mark D.
Apr 2, 2018

#3/2#

Explanation:

If two lines are perpendicular then the result of multiplying the two gradients together always equals -1

Rearrange the equation to find the gradient:

#3y +2x = 6#

#=># #3y = -2x +6#

#=># #y = -2/3x +2#

Gradient = #-2/3# the reciprocal is #3/2#

#-2/3 xx 3/2 = -1#

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