Algebra · Straight-line graphs
Chapter 1 · 4
The idea
Parallel and perpendicular lines
Why parallel lines share a gradient (and nothing else), why perpendicular gradients multiply to −1 (the negative reciprocal), and how to build a line through a given point with either condition.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
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Algebra · Straight-line graphs
Parallel and perpendicular lines
Why parallel lines share a gradient (and nothing else), why perpendicular gradients multiply to −1 (the negative reciprocal), and how to build a line through a given point with either condition.
Why it works
Parallel: same gradient
Parallel = same steepness = same gradient. Two lines that never meet climb at the same rate: and are parallel — same , different . The intercept is irrelevant to parallelism; it just slides the line up or down. So "parallel to through " is instant: keep , read the new intercept: .Perpendicular: the negative reciprocal
Turning a line through 90° swaps its rise and run AND flips one sign: a gradient of (right 1, up 4) becomes right 4, DOWN 1 — gradient . In general:Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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