Question

The graph shows that while it was being filled, the amount of water in gallons in a swimming pool was approximately proportional to the time that has passed in minutes.

Estimate the constant of proportionality for the gallons of water per minute going into the pool.

Answer 1

To estimate the constant of proportionality for the gallons of water per minute going into the pool, you'll need to look at the graph and find two points that lie on the line.

Let's say you identify two points on the line, (t1, g1) and (t2, g2), where t represents time in minutes and g represents the gallons of water.

The constant of proportionality (k) can be calculated using the formula:

\[k = \frac{g2 - g1}{t2 - t1}\]

This represents the rate of change of gallons of water per minute.

Keep in mind that this is an estimate based on the data points you choose. If possible, try to choose points that are well-distributed along the line to get a more accurate estimate of the constant of proportionality.

Explanation: