Create an equation that represents a line that is perpendicular to a line with a slope -2?

(first step:

you must remember the following theorem :

Two lines whose slopes are m1 and m2, are perpendicular if and only if m1m2 = -1

(second step

you have one slope given and it  is -2 then you  substitute in the previous equation

(third step

m1*-2=-1⇒m1=-1/-2⇒m1= 1/2

it means that new slope of the equation is 1/2

(for step

with a given point and a  the slope you can build the equation that is perpendicular to a line with slope -2

the equation point- slope is

y-y1=m(x-x1)

with any given point as (2,-5) substitute it in the previous equation

[y-(-5)]=  1/2(x-2)⇒ (y+5) = 1/2x-1/4⇒y-1/2x+5+1/4⇒y-1/2x+21/4 =0

(five step

you must look for the value of x in the following equation

y-1/2x+21/4 =0

where, y = 1/2X-21/4  and this is the equation that represents a line that is perpendicular to a line with slope -2