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Two lines are perpendicular if the product of their slopes is -1.

A straight line with an equation in the form:

y = mx + c

has slope m and y-intercept c.

Given two lines y = mx +c and y = nx + d they are perpendicular if mn = -1.

Examples:

1) are the two lines y = 2x and 2y = x + 2 perpendicular?

y = 2x

2y = x + 2 → y = 1/2 x + 1

→ product of slopes = 2 x 1/2 = 1 → the lines are not perpendicular

2) are the two lines y + 2x = 5 and 2y = x + 2 perpendicular?

y + 2x = 5→ y = -2x + 5

2y = x + 2 → y = 1/2 x + 1

→ product of slopes = -2 x 1/2 = -1 → the lines are perpendicular

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