Question

• 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.

Answer 1

`y=6x`

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
`y/x=k` or
`y=kx`

Looking at the graph

take the points

(2,12),(4,24)

Find the value of the constant of proportionality k

`k=y/x`

For the point (2,12) ---->
`k=12/2=6`

For the point (4,24) ---->
`k=24/4=6`

The value of k=6 gal/min

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

The equation for this relationship is

`y=6x`