problems 1 - 3: this graph shows the amount of water in a swimming pool as it fills up.\n1. explain how the…

problems 1 - 3: this graph shows the amount of water in a swimming pool as it fills up.\n1. explain how the graph shows that the relationship between time and the amount of water is proportional.\n2. calculate a constant of proportionality for this relationship.\n3. this pool is safe to swim in when it contains 9,000 gallons of water. how long will it take to fill the pool to this level?

Answer

Explanation:

Step1: Check proportionality

A proportional relationship has a straight - line graph passing through the origin. Looking at the graph (assuming it is a straight - line passing through the origin as per the nature of proportional relationships in such problems), the points lie on a straight line and when time (t = 0), water (w=0).

Step2: Calculate constant of proportionality

Let's take a point ((t,w)) from the graph. Suppose we take the point ((10,150)) (assuming the scale of the graph, if (x) - axis has a scale of (10) units per major tick and (y) - axis has a scale of (150) units per major tick for the first non - zero point). The constant of proportionality (k=\frac{w}{t}). Substituting (t = 10) and (w = 150), we get (k=\frac{150}{10}=15) (gal/min).

Step3: Find time to fill 9000 gallons

We know that (w=kt), where (w = 9000) and (k = 15). Rearranging the formula for (t), we get (t=\frac{w}{k}). Substituting (w = 9000) and (k = 15), we have (t=\frac{9000}{15}=600) minutes.

Answer:

The graph is a straight - line passing through the origin, which shows a proportional relationship.
The constant of proportionality is (15) gal/min.
It will take (600) minutes to fill the pool.