Question

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

Answer 1

Answer: 2x - y = 0

Step-by-step explanation: 2x - y = 0 is correct. The given line has slope - 1 /2 , so line L must have slope 2. Solving choice B for y yields y = 2x, which passes through the origin.

Answer 2

x + 2y = 8 could be written as 2y=8-x or y = -(1/2) x +8

L is passing through the origin, so her equation is y₁ =mx.

Calculating a (its coefficient or slope) will solve the problem.

We know that L (represented by y₁) is perpendicular to y = -(1/2) x +8
We know also that 2 lines to be perpendicular, the product of their slope
(m₁ & m₂) should be equal to - 1
In our case the 1st slope is (-1/2) & the 2nd slope is m, hence
(-1/2) *m = -1===> m =2
& the equation of line L=2x