Answer:
The required function is [tex]y=18-4x[/tex] and the graph of the function is shown below.
Step-by-step explanation:
It is 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.
It means the initial liquid in tank is 17 gallons and rate of change is 4 gallons per hour.
y-intercept is (0,18).
Slope is -4.
The liquid in tank is defined by the function
[tex]y=18-4x[/tex] [tex][\because y=mx+b][/tex]
At y=0 the tank will empty.
[tex]0=18-4x[/tex]
[tex]x=4.5[/tex]
The x-intercept is (4.5,0).
Therefore the required function is [tex]y=18-4x[/tex] and the graph of the function is shown below.
