Question

at 4:00 am,there were 800,000 gallons of water remaining at a reservoir.after 4 hours of irrigation,there were 100,000 gallons of water remaining.write an equation that describes the number of gallons of water as a function of the time the field has been irrigated

Answer 1

Let the
`x-axis` presents the time, and the
`y-axis` the gallons of water remaining, so our first point will be (4,800000). We know from the problem that after 4 hours, at 8:00 am, there were 100000 gallons, so our second point will be (8,100000).
To relate those two points we are going to use the point slope formula:

`m= (y_(2)-y_(1) )/(x_(2)-x_(1) )`
where

`x_(2)` is 8

`x_(1)` is 4

`y_(1)` is 800000

`y_(2)` is 100000

So,
`m= (100000-800000)/(8-4)`

`m= (-700000)/(4)`

`m=-175000`

Now that we have our slope, we are going to use the point-slope formula to find our equation:

`y-y_(1) =m(x-x_(1) )`

`y-800000=-175000(x-4)`

`y-800000=-175000x+700000`

`y=-175000x+1500000`

The equation that describes the number of gallons of water as a function of the time the field has been irrigated is
`y=-175000x+1500000`
where

`y` are the remaining gallons of water in the reservoir after
`x` hours

`x` is the time the field has been irrigated in hours