Question

how do you do this?

find equations in standard form of the lines through point P that are (a) parallel to, and (b) perpendicular to line L:

1) P(0,-4); L: 2y=x
2)P(2,0);L:x+2y=3
3)P(-4,1); L: y+2=0

Answer 1

I will do one of them #2, you try the others

from x + 2y = 3
2y = -x + 3
y = -1/2x + 3/2

so the slope of a parallel line must be -1/2 and the slope of a perpendicular line must be 2

Parallel line: y = -1/2x + b
but (2,0) is the y-intercept, so the equation is y = -1/2x

perpendicular line: using y = mx + b
we know slope is 2 and b = 0
so y = 2x