The table shows the water level y, in metres, in a reservoir x weeks into a drought. Which equation models the relationship?

Question

x (weeks): 1, 2, 3, 4
y (metres): 8, 6.5, 5, 3.5

Accepted Answer

A. y = 9.5 − 1.5x. The level falls by 1.5 each week (a constant change, so linear). At x = 1, y = 8, so y = 9.5 − 1.5x. Check x = 4: 9.5 − 6 = 3.5 ✓.

Answer

B. y = 8 − 1.5x — 8 − 1.5x gives 6.5 at x = 1, not 8; 8 is the value at x = 1, not x = 0.

Answer

C. y = 8(0.8)ˣ — An exponential model would give changes that shrink each week; these are constant.

Answer

D. y = 9.5 − x — A slope of −1 gives 8.5 at x = 1.

Problem-Solving and Data Analysis practice question