Question

Find equations in standard form of the lines through point P that are A.) parallel to, and B.) perpendicular to, line L. P(0,-4); L: 2y=x. I've tried solving it and looking at examples, but no examples in my book are like this problem.

Answer 1

2y = x
y = 1/2x....the slope of this line is 1/2.

A parallel line will have the same slope.
y = mx + b
slope(m) = 1/2
(0,-4)....x = 0 and y = -4
now we sub and find b, the y int
-4 = 1/2(0) + b
-4 = b
so ur equation is : y = 1/2x - 4...but we need it in standard form Ax + By = C

y = 1/2x - 4....subtract 1/2x from both sides
-1/2x + y = -4...multiply both sides by -2
x - 2y = 8 <== standard form of parallel line
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the slope of the line was 1/2. A perpendicular line will have a negative reciprocal slope. All that means is flip the slope and change the sign. So our perpendicular line will have a slope of -2...see how I flipped 1/2 making it 2/1...and changed the sign, making it -2.

y = mx + b
slope(m) = -2
(0,-4)...x = 0 and y = -4
sub and find b
-4 = -2(0) + b
-4 = b
so this equation is : y = -2x - 4....but we need standard form

y = -2x - 4....add 2x to both sides
2x + y = -4 <== standard form of perpendicular line