How do you find a standard form equation for the line with (-1,-2) ; perpendicular to the line 2x+5y+8=0?

1 Answer
Mar 31, 2017

Answer:

#2y-5x-1=0#
or
#5x-2y+1=0#

Explanation:

Always keep in mind that when two lines are perpendicular, the product of their slopes is -1.

Proof :-
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slope intercept equation of a straight line is given as:-
#y = mx+c#
#-># #m=# slope
#-># #c=# y intercept (y coordinate of the point where the line intersects the y axis) which is a constant for a given line.

given line #2x+5y+8=0# can be written as
#5y=-8-2x# #=># #y=-2/5x - 8/5#
comparing with slope intercept form, slope #m_1=-2/5#
let slope of second line be #m_2#.
#therefore# #m_1*m_2 = -1# (given lines are perpendicular)
#implies m_2 = 5/2#

#therefore # equation of line we have to find is given by:-

#y=5/2x+c_2# where

since it passes through #(-1,-2)# substituting this point in the equation,
#-2=5/2(-1)+c_2#
#implies c_2= 5/2-2 = 1/2#

hence equation becomes,
#y=5/2x+1/2#
#i.e. 2y-5x-1=0#

Hence required equation is #2y-5x-1=0# or #5x-2y+1=0#