•the graph shows the relationship between the gallons of water a sprinkler
system uses and the number of minutes the system is used. write an
equation for this relationship. explain how you determined your answer.

Step-by-step explanation:

Let

x ----> the number of minutes

y ----> the gallons of water

we know that

The graph shows a proportional relationship , because is a line that passes through the origin

so

A proportional variation can be expressed in the form or

Looking at the graph

take the points

(2,12),(4,24)

Find the value of the constant of proportionality  k

For the point (2,12) ---->

For the point (4,24) ---->

The value of k=6 gal/min

That means ----> The system uses 6 gallons of water per minute

The equation for this relationship is