Finding y = ax + b from two facts

A linear relationship between two variables can be written y = ax + b. For the tiles, with x the stage and y the number of tiles, y = 2x – 1.

"Two facts, two unknowns." A data plan bills ₹350 for 10 GB and ₹550 for 20 GB. Put both into y = ax + b:

• 350 = 10a + b
• 550 = 20a + b

Subtract the first from the second: 200 = 10a, so a = 20. Then b = 350 – 10 × 20 = 150. So y = 20x + 150.

Read what the numbers mean. 20 is what each extra GB costs (₹20 per GB). 150 is what you pay with no data at all: the fixed monthly fee. Again, a fixed part plus a per-item part.

The same method converts temperatures. °C = a°F + b, with 0 °C = 32 °F and 100 °C = 212 °F, gives 180a = 100, so a = 5/9 and b = –160/9.