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 = 29x + 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? 300 liters (b) what is the change per minute in the amount of water in the pond? liters

Explanation:

Part (a)

Step1: Recall the slope - intercept form of a linear equation

The slope - intercept form of a linear equation is $y = mx + b$, where $b$ is the y - intercept (the value of $y$ when $x = 0$) and $m$ is the slope (the rate of change of $y$ with respect to $x$).
In the given equation $y=29x + 300$, when $x = 0$ (which represents the starting time, 0 minutes of water being added), we substitute $x = 0$ into the equation:
$y=29(0)+300$

Step2: Calculate the value of $y$ when $x = 0$

$y = 0+300=300$. So the starting amount of water in the pond is 300 liters.

Part (b)

Step1: Recall the meaning of the slope in a linear equation

In the linear equation $y=mx + b$, the coefficient $m$ of $x$ represents the rate of change of $y$ with respect to $x$. In the context of this problem, $y$ is the amount of water in liters and $x$ is the number of minutes.
The given equation is $y = 29x+300$, so the coefficient of $x$ is 29.

Step2: Interpret the slope

Since the coefficient of $x$ is 29, this means that for each increase of 1 in $x$ (each additional minute), $y$ (the amount of water) increases by 29 liters. So the change per minute in the amount of water in the pond is + 29 liters (or just 29 liters, since it's an increase).

Answer:

s:
(a) The starting amount of water in the pond is $\boldsymbol{300}$ liters.
(b) The change per minute in the amount of water in the pond is $\boldsymbol{29}$ liters.