Question

A vat contains 18 gallons of liquid when a drain pipe opens and the liquid begins to leave the vat at a rate of 4 gallons per hour.

Use the Line Tool to graph the amount of liquid remaining in the vat at any hour, x.

Answer 1

`y=-4x+18`

Explanation:

Let x be the number of hours.

We have been given that a vat contains 18 gallons of liquid when a drain pipe opens and the liquid begins to leave the vat at a rate of 4 gallons per hour.

To graph the amount of liquid first of all we will find the equation of line for our given situation.

Since we know that equation of a line in slope-intercept form is:
`y=mx+b`, where, m = slope and b = y-intercept or initial value.

As liquid is leaving the vat at a rate of 4 gallons per hour, this means that amount of liquid in vat in decreasing 4 gallons per hour. As slope is also known as rate of change, so slope of our given line will be -4. A negative slope means that with each increase in x our y will decrease by 4.

As initially there were 18 gallons of liquid in vat, so our y-intercept will be 18.

Upon substituting our given values in slope-intercept form of equation we will get,

`y=-4x+18`

Let us find x-intercept by substituting y=0 in our equation.

`0=-4x+18`

`4x=18`

`(4x)/(4)=(18)/(4)`

`x=4.5`

Now we will draw a line connecting our y-intercept and x-intercept from (0,18) to (4.5,0).

Please find the attachment for the graph of the given line.