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

Answer:

$y=-4x+18$

Step-by-step 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.

$0=-4x+18$

$4x=18$

$\frac{4x}{4}=\frac{18}{4}$  

$x=4.5$

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.