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 = 20x + 300. 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? (square) liters (b) what is the change per minute in the amount of water in the pond? (square) liters

Explanation:

Part (a)

Step1: Recall slope - intercept form

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value). In the given equation $y=20x + 300$, when $x = 0$ (the starting time, i.e., 0 minutes), we can find the starting amount of water.

Step2: Calculate starting amount

Substitute $x = 0$ into the equation $y=20x + 300$. We get $y=20(0)+300=300$. So the starting amount of water in the pond is 300 liters.

Step1: Recall slope - intercept form

In the equation $y = mx + b$, $m$ represents the rate of change. In the equation $y = 20x+300$, the coefficient of $x$ is 20. Since $x$ represents the number of minutes and $y$ represents the amount of water in liters, the value of $m$ (20) represents the change in the amount of water per minute. Since the pond is being filled with water, the change is positive.

Answer:

300

Part (b)