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Linear Equations and Graphs

Parallel and Perpendicular Lines

T wo lines are parallel if they have the same slope. Parallel lines never intersect. The lines shown below are parallel

The lines y = 4x, y = 4x + 5 and y = 4x - 100 are also parallel as they all have slope 4.

Perpendicular lines are lines that intersect at right angles (90 degrees). By using Pythagoras’s Theorem it can be shown that two lines with slopes m₁ and m₂ are perpendicular if  m₁×m₂ = -1. (Click here to see details.) Hence the slopes are negative reciprocals. That is m₁ = -1/m₂.

Exercise 9.

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