1. The equation of the parallel line is y = -x - 1.
2. The equation of the perpendicular line is y = 3/2x - 4.
What are the Equations of Parallel and Perpendicular Lines?
Lines that are parallel have the same slope while slope values for perpendicular lines are negative reciprocals.
1. The slope (m) of y = -x + 1 is -1. Substitute m = -1 and (x, y) = (4, -5) into y = mx + b:
-5 = -1(4) + b
-5 = -4 + b
-5 + 4 = b
b = -1
Substitute b = -1 and m = -1 into y = mx + b
y = -x - 1
2. The slope (m) of y = -2/3x + 5 is -2/3.
Negative reciprocal of -2/3 is 3/2.
Substitute m = 3/2 and (x, y) = (2, -1) into y = mx + b:
-1 = 3/2(2) + b
-1 = 3 + b
-1 - 3 = b
b = -4
Substitute b = -4 and m = 3/2 into y = mx + b
y = 3/2x - 4
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