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

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