Question

Find the equation of the line that passes through (−2,5) and is perpendicular to the line
2x + y = 5 . Write your answer in slope-intercept form.

Answer 1

if a line is perpedicular to another line, the product of their slopes will equals to -1

suppose m is the slope.
from 2x + y = 5 -> y=-2x+5 , we get m1= -2
m1*m2 = -1
(-2) * m2 =-1 -> m2= 1/2

so the slope of the other line is 1/2

then the equation of the other line will be y=(1/2)x +b
we know that the line passes through (−2,5)
so -> 5=(1/2)(-2) + b
5=-1+b -> b=6
hence the equation of the line is y=(1/2)x + 6