Question

What is the equation of the line that passes through the point (4, 1) and is perpendicular to the line y = –2x + 4?

Answer 1

slope of y = –2x + 4 is -2
slope of the required line is (-1)/(-2) =1/2 as they are perpendicular
let the equation of the required line be y=2x+c where c is a constant
as the line passes through (4,1) which means that (4,1) suits the equation
put x=4 and y=1 into y=2x+c
1=(1/2)(4)+c
c=-1
therefore, the required equation is y=(x/2)-1