What is the equation of the line that passes through #(-4,1)# and is perpendicular to the line that passes through the following points: #(6,9),(-2,6) #?

1 Answer
Shwetank Mauria
Mar 7, 2016

#8x+3y+29=0#

Explanation:

Slope of the line that passes through points #(x_1,y_1)# and #(x_2,y_2)# is given by #(y_2-y_1)/(x_2-x_1)#. Hence slope of line joining #(6,9)# and #(−2,6)# is #(6-9)/((-2)-6)# or #-3/-8=3/8#.

As product of slope of two perpendicular lines is #-1#, slope of line perpendicular to one joining #(6,9)# and #(−2,6)# is #-1/(3/8)# or #-8/3#.

Now using Point-slope form, the equation of line passing through #(-4,1)# and slope #-8/3# will be

#(y-1)=-8/3xx(x-(-4))# or

#3(y-1)=(-8)xx(x+4)# or

#3y-3=-8x-32# or #8x+3y+29=0#

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