Question

owners of a recreation area are filling a small pond with water. let y represent the total amount of water in the pond (in liters). let x represent the total number of minutes that water has been added. suppose that x and y are related by the equation y = 500 + 33x. answer the questions below. note that a change can be an increase or a decrease. for an increase, use a positive number. for a decrease, use a negative number. (a) what was the starting amount of water in the pond? liters (b) what is the change per minute in the amount of water in the pond? liters

Explanation:

Step1: Analyze the linear equation form

The equation \(y = 500+33x\) is in the slope - intercept form \(y = b + mx\), where \(b\) is the \(y\) - intercept (initial value) and \(m\) is the slope (rate of change).

Step2: Find the starting amount

For the starting amount of water, we set \(x = 0\). Substituting \(x = 0\) into \(y=500 + 33x\), we get \(y=500+33\times0=500\).

Step3: Find the rate of change

The coefficient of \(x\) in the equation \(y = 500+33x\) is the rate of change. Here, the coefficient of \(x\) is \(33\).

Answer:

(a) \(500\) liters
(b) \(33\) liters