Direct Variation y = kx

Pre-Algebra · Axiom Academy

When two quantities move together at a fixed rate, y = kx — a straight line through the origin with slope k . Two quantities vary directly when they grow together at a constant rate: as one doubles, the other doubles; as one triples, the other triples. We write this as y = kx . k is the constant of proportionality (the slope) 2. The Constant k Is the Ratio y / x Pick any point (x, y) on a direct variation and divide y by x . You always get the same number — that number is k . Different points, identical ratio. holds for every point on the line, not just one. k tells you the amount of y per single unit of x . Know one matching pair (x, y) ? Then . With k in hand, y = kx gives y for any new x . Suppose y = 12 when x = 3 . Divide to find the constant: 3. Double x, Double y — Using It Because y = kx , scaling x scales y by the same factor: replace x with 2x and y = k(2x) = 2(kx) — exactly double . This is why direct variation models so many everyday situations. A car travels 60 miles in 1 hour at a steady speed. First find k (the speed), then use y = kx to reach 3 hours: Example: scaling up from a known point y varies directly with x , and y = 18 when x = 6 . Find y when x = 10 : Direct variation shows up all over the place — the same one formula behind each: You've seen direct variation three ways: a straight line out of the origin, a ratio y/x that never changes, and a rule where doubling x doubles y . Scroll up to revisit any step.

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