How do you find the equation of the line that is perpendicular to #2y=-5x# and passing through #(10, -5)#?

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Answer 1 · 2017-02-24T09:11:52

#y =2/5 x - 9# or #5 y =2 x - 45#

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

let say #m# is the gradient/slope of perpendicular to the line equation where it slope is #=-5/2#.

therefore,
#m * -5/2 = -1#, #m = 2/5#.

The linear equation, #(y-y_1) =m(x-x_1)# where #x_1 = 10 and y_1 = -5#

therefore,
#(y- (-5)) =2/5 (x-10)#

#y+5 =2/5 x - 4#

#y =2/5 x - 4-5#

#y =2/5 x - 9# or #5 y =2 x - 45#