Parallel and Perpendicular Lines

Pre-Algebra · Axiom Academy

LESSON Parallel and Perpendicular Lines One number — the slope — decides whether two lines run side by side forever or cross at a perfect right angle. Every straight line has one steepness number, its slope m . Move one step to the right along the line and the slope tells you how far it climbs (the rise ) for that one-step run . Watch a point travel up y = 2x : each run of 1 buys a rise of 2 , so m = 2 . slope = how much it rises per step to the right 2. Parallel Lines Share a Slope Two lines are parallel when they never meet. If both rise at the exact same rate, the vertical gap between them can never close — so the test is simply equal slopes . Below, and both have ; the sweeping ruler shows their gap holding steady at 3 the whole way across. same slope, different intercept parallel y = -3x + 2 and y = -3x + 5 are parallel (both m = -3 ). But y = -3x + 2 and y = -3x + 2 are the same line, not parallel — parallel lines need equal slopes and different intercepts . 3. Perpendicular Lines Flip and Negate Two lines are perpendicular when they cross at a right angle. Rotating a line's rise/run triangle by swaps the run and the rise and flips one sign — so the new slope is the negative reciprocal . Watch the triangle on y = 2x pivot a quarter-turn and land exactly on . Flip the fraction: a slope of becomes . Change the sign: becomes . Their product is — the signature of a right angle. You can now classify any pair of lines from their slopes alone — no graph required.

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