Q1.
Can you guess what the numbers 20 and 150 in the equation y = 20x + 150 represent?
Answer
20 = the charge per GB of data, in rupees
150 = the fixed monthly fee, in rupees
150 = the fixed monthly fee, in rupees
Why they must mean that: read the equation at two special inputs.
• Put x = 0. Then y = 150 — the bill for a month in which no data is used at all. Only the fixed fee can survive, so 150 is that fee.
• Increase x by 1. Then y increases by 20(x + 1) + 150 − (20x + 150) = 20, whatever x was. One more GB always costs ₹20, so 20 is the rate per GB.
These are exactly the roles of slope and y-intercept: 20 is the slope (change per unit) and 150 the y-intercept (starting value).
• Put x = 0. Then y = 150 — the bill for a month in which no data is used at all. Only the fixed fee can survive, so 150 is that fee.
• Increase x by 1. Then y increases by 20(x + 1) + 150 − (20x + 150) = 20, whatever x was. One more GB always costs ₹20, so 20 is the rate per GB.
These are exactly the roles of slope and y-intercept: 20 is the slope (change per unit) and 150 the y-intercept (starting value).
Check it yourself: at 10 GB, 20(10) + 150 = ₹350 and at 20 GB, 20(20) + 150 = ₹550, which are the two bills the student actually observed. ✓