x + 2y = 3
2y = -x + 3
y = -1/2x + 3/2.....slope to this is -1/2
parallel lines will have the same slope.
y = mx + b
slope(m) = -1/2
(-2,5)...x = -2, and y = 5
sub to find b, the y int
5 = -1/2(-2) + b
5 = 1 + b
5 - 1 = b
4 = b
so ur parallel equation is : y = -1/2x + 4
perpendicular lines will have negative reciprocal slopes. To find the negative reciprocal of a number, u just flip the number and change the sign. So our slope was - 1/2.....the negative reciprocal would then be 2 (see how I flipped -1/2 making it -2/1 or just - 2...then changed the sign, making it 2)
y = mx + b
slope(m) = 2
(-2,5)...x = -2 and y = 5
sub and find b
5 = 2(-2) + b
5 = -4 + b
5 + 4 = b
9 = b
so ur perpendicular equation is : y = 2x + 9
