Let
x-------> the time in minutes
y-----> the function that represent the amount of water in gallons
Step 1
Find the x-intercept
we know that
The x-intercept is the value of x when the value of the function is equal to zero
In this problem (see the graph)
For [tex]y=0[/tex]
the value of x is [tex]15\ min[/tex]
so
the x-intercept is the point [tex](15,0)[/tex]
that means
The number of minutes it takes for the container to empty is [tex]15\ min[/tex]
Step 2
Find the y-intercept
we know that
The y-intercept is the value of the function y when the value of x is equal to zero
In this problem (see the graph)
For [tex]x=0[/tex]
the value of the function y is [tex]120\ gal[/tex]
so
the y-intercept is the point [tex](0,120)[/tex]
that means
The number of gallons in the container before the drain is open is [tex]120\ gal[/tex]
therefore
the answer in the attached figure
