Introduction to Linear Polynomials
Linear patterns
Spot patterns that grow in equal steps, and the linear polynomial behind them.
A square's perimeter is 4x for side x. Sides 1, 1.5, 2, 2.5 and 3 cm give perimeters 4, 6, 8, 10 and 12 cm. Each time the side grows by 0.5 cm, the perimeter grows by 2 cm, always the same amount.
A chess club charges ₹200 to join plus ₹50 a match. Think of it as a fixed part plus a per-match part:
- 1, 2, 3, 4, 5 matches cost ₹250, 300, 350, 400, 450;
- m matches cost ₹(200 + 50m).
Each extra match adds the same ₹50.
This is what makes a polynomial linear: the difference between one value and the next is constant. Such patterns are called linear patterns.
Work backwards too. A player paid ₹750, so 200 + 50m = 750. Take away the fixed part: 50m = 550, so m = 11 matches. Check: 200 + 550 = 750.
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