Question

Line L is perpendicular to the line with equation x + 2y = 8 and passes through the origin. Determine the equation of line L.

A) x - 2y = 0
B) 2x - y = 0
C) 2x - y = -8
D) x - 2y = -8

Answer 1

x+2y=8

2y=-x+8

y=-x/2+4

So for L to be perpendicular to this its slope must be the negative reciprocal of y's slope...

-1m/2=-1, m=2

So L has a slope of 2

L=2x+b, since it passes through the origin its y-intercept is zero so

L=2x or back in y terms

y=2x, by convention you want to arrange this so x has a positive coefficient...

2x-y=0

So B, is the correct answer.

Answer 2

B) 2x-y=0
You solve for y to get a linear equation. (y=-1/2 x+4)  Then you know that perpendicular lines have opposite slopes and it passes through the origin.  so in the form y=Mx+B, b is 0, and m is 2.  y=2x+0. then subtract y and you get 0=2x-y