Question

Luis is filling his half-empty swimming pool with water at a rate of 220 gallons per hour. After 33 hours the pool contains 855 gallons of water. What is the equation in point-slope form that relates the amount of water in the pool, y, to the number of hours, x, that Luis has been filling the pool?

What is the equation in standard form?

Answer 1

`y - 220x = -6405`

Explanation:

Given

`Rate = 220`

At
`time = 33\ hours`,
`gallons = 855`

Required

Determine the equation

The rate means slope (m).

So:

`m = 220`

From the question, x represents time and y represents the amount of water.

So:

`x=33` when
`y = 855`

Or:

`(x_1,y_1) = (33,855)`

The equation is determined using:

`y - y_1 = m(x - x_1)`

This gives:

`y - 855 = 220(x - 33)`

`y - 855 = 220x - 7260`

Collect Like Terms

`y - 220x = 855 - 7260`

`y - 220x = -6405`

Hence, the equation in standard form is:

`y - 220x = -6405`