Find standard form equation of line through P that are parallel and perpendicular to line L? URGENT!!!!!!!!!!!

Question

P(0, -4) L: 2y=x

All i could get is y = 2/x....

How can I finish this problem????

Also for this one also...please help

P(-1, 2) L: x-3y=2

all i got for it was y = (x+2)/3

Answer 1

Line: 2y = x
y = x/2

The slope of the line is m = 1/2. A parallel line will have the same slope. Put it thru the point P(0, -4) and you get:

y + 4 = (1/2)(x - 0)
y + 4 = (1/2)x
y = (1/2)x - 4
____________

The slope of a perpendicular line to the given line is the negative reciprocal.

m' = -1/m = -1/(1/2) = -2

Now put a line of that slope thru P(0, -4).

y + 4 = -2(x - 0)
y +4 = -2x
y = -2x - 4
__________