Question

1. higher order thinking you use a garden hose to fill a circular wading pool that is 83.6 cm deep. you measure the depth of the water in the pool every 2 minutes. the table shows the data.

a. what is the slope of the line that represents the change in the depth of the water?
b. what does this slope mean?
c. how many minutes will it take to fill the pool?

Explanation:

Step1: Calculate the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(2,4.4)\).
\(m=\frac{4.4 - 0}{2 - 0}\)
\(m = 2.2\)

Step2: Interpret the slope

The slope \(m = 2.2\) means that the depth of the water in the pool increases by \(2.2\) cm per minute.

Step3: Find the time to fill the pool

We know that the depth of the pool is \(y = 83.6\) cm and the slope \(m=2.2\) (where \(y=mx\), \(x\) is the time).
From \(y = mx\), we can solve for \(x\). Substitute \(y = 83.6\) and \(m = 2.2\) into the equation \(x=\frac{y}{m}\)
\(x=\frac{83.6}{2.2}\)
\(x = 38\)

Answer:

a. The slope is \(2.2\).
b. The depth of water increases by \(2.2\) cm per minute.
c. It will take \(38\) minutes to fill the pool.