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- Direct and inverse proportion, and original values
Direct and inverse proportion, and original values
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Some quantities grow together; others share out, so one falls as the other rises. Knowing which is which is the key.
Direct proportion
y is directly proportional to x when y = kx for a number k.
The graph is a straight line through the origin.
y = 12 when x = 4, so k = 3. When x = 10, y = 30.
The graph is a straight line through the origin.
y = 12 when x = 4, so k = 3. When x = 10, y = 30.
Inverse proportion
y is inversely proportional to x when y = kx. When one doubles, the other halves.
The graph is a curve that gets closer and closer to the axes.
6 workers take 10 days: that is 60 worker-days. 4 workers take 60 ÷ 4 = 15 days.
The graph is a curve that gets closer and closer to the axes.
6 workers take 10 days: that is 60 worker-days. 4 workers take 60 ÷ 4 = 15 days.
Finding the original value
After a percentage change, divide by the multiplier to get back to the original.
After a 20% increase a price is £54. Original = 54 ÷ 1.2 = £45.
After 15% off a coat costs £68. Original = 68 ÷ 0.85 = £80.
After a 20% increase a price is £54. Original = 54 ÷ 1.2 = £45.
After 15% off a coat costs £68. Original = 68 ÷ 0.85 = £80.
y is inversely proportional to x. y = 8 when x = 3. Find y when x = 12.
- k = x × y = 3 × 8 = 24
- y = 2412
Answer: y = 2
Direct: y = kx, a straight line through the origin. Inverse: y = k ÷ x, so one doubles as the other halves. For original values, divide by the multiplier.
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