How can you use the equations of two non-vertical lines to tell wether the lines are parallel or perpendicular?

Answer 1

-- Rearrange the equation of Line #1 into the form y1 = A1x1 + B1

-- Rearrange the equation of Line #2 into the form y2 = A2x2 + B2

-- Compare the constants A1 and A2.

If A1 = A2, then the lines are parallel.

If A1 = -1/A2, then the lines are perpendicular.
Get them both into the form: y = mx + c.

If they are parallel then their gradients (given by m in the equation above) will be equal.

If they are perpendicular, then the product of their gradients will be -1.

Examples:

• 2y = 4x + 5, y - 2x = 6

2y = 4x + 5 → y = 2x + 5/2 → gradient = 2

y - 2x = 6 → y = 2x + 6 → gradient = 2

The gradients are equal, thus the lines are parallel

• 2y = x + 4, y + 2x = 3

2y = x + 4 → y = 1/2 x + 2 → gradient = 1/2

y + 2x = 3 → y = -2x + 3 → gradient = -2

Product of gradients is 1/2 x -2 = -1, thus the lines are perpendicular.