Question

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.

Answer 1

The equation in the function form is f(x) = -3x + 15 and the tub started with 15 gallons of water.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have an equation:

y –12 = –3(x – 1)

We can write the above equation as follows:

y = 12 - 3(x - 1)

y = 12 - 3x + 3

y = -3x + 15

or

f(x) = -3x + 15

Plug x = 0

f(0) = 15

The tub started with 15 gallons of water.

Thus, the equation in the function form is f(x) = -3x + 15 and the tub started with 15 gallons of water.

Learn more about the function here:

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