A tub of water is emptied at a rate of 3 gallons per minute. The equation y –12 = –3(x – 1) models the amount of water remaining, where x is time (in minutes) and y is the amount of water left (in gallons). Analyze the work shown below to determine the initial amount of water.

1. Solve for the y-variable.

y – 12 = –3(x – 1)

y – 12 = –3x + 3

y = –3x +15

2. Write the equation using function notation.

f(x) = –3x +15

The tub started with ______ gallons of water.

1 answer

The tub started with 15 gallons of water.

Explanation: In the equation y = -3x + 15, the y-variable represents the amount of water remaining. So, the initial amount of water can be found by plugging in x = 0 (initial time) into the equation:

y = -3(0) + 15
y = 15

Therefore, the tub started with 15 gallons of water.