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 \(x\) be the time (minutes) and \(y\) be the depth of water (cm). Take two points \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(2,4.4)\). Then \(m=\frac{4.4 - 0}{2-0}\).

$$m = 2.2$$

Step2: Interpret the slope

The slope \(m = 2.2\) means that for every 1 - minute increase in time, the depth of water in the pool increases by \(2.2\) cm.

Step3: Find the time to fill the pool

The pool is \(83.6\) cm deep. We know that the relationship between depth \(y\) and time \(x\) is \(y = 2.2x\) (since \(y=mx + b\) and \(b = 0\) when \(x = 0,y=0\)). We want to find \(x\) when \(y = 83.6\). So, \(x=\frac{y}{m}\), substituting \(y = 83.6\) and \(m=2.2\) gives \(x=\frac{83.6}{2.2}\).

$$x = 38$$

Answer:

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